3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that is requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
213 C<isl> is released under the MIT license.
217 Permission is hereby granted, free of charge, to any person obtaining a copy of
218 this software and associated documentation files (the "Software"), to deal in
219 the Software without restriction, including without limitation the rights to
220 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
221 of the Software, and to permit persons to whom the Software is furnished to do
222 so, subject to the following conditions:
224 The above copyright notice and this permission notice shall be included in all
225 copies or substantial portions of the Software.
227 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
228 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
229 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
230 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
231 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
232 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
237 Note that by default C<isl> requires C<GMP>, which is released
238 under the GNU Lesser General Public License (LGPL). This means
239 that code linked against C<isl> is also linked against LGPL code.
241 When configuring with C<--with-int=imath>, C<isl> will link against C<imath>, a
242 library for exact integer arithmetic released under the MIT license.
246 The source of C<isl> can be obtained either as a tarball
247 or from the git repository. Both are available from
248 L<http://freshmeat.net/projects/isl/>.
249 The installation process depends on how you obtained
252 =head2 Installation from the git repository
256 =item 1 Clone or update the repository
258 The first time the source is obtained, you need to clone
261 git clone git://repo.or.cz/isl.git
263 To obtain updates, you need to pull in the latest changes
267 =item 2 Optionally get C<imath> submodule
269 To build C<isl> with C<imath>, you need to obtain the C<imath>
270 submodule by running in the git source tree of C<isl>
275 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
277 =item 2 Generate C<configure>
283 After performing the above steps, continue
284 with the L<Common installation instructions>.
286 =head2 Common installation instructions
290 =item 1 Obtain C<GMP>
292 By default, building C<isl> requires C<GMP>, including its headers files.
293 Your distribution may not provide these header files by default
294 and you may need to install a package called C<gmp-devel> or something
295 similar. Alternatively, C<GMP> can be built from
296 source, available from L<http://gmplib.org/>.
297 C<GMP> is not needed if you build C<isl> with C<imath>.
301 C<isl> uses the standard C<autoconf> C<configure> script.
306 optionally followed by some configure options.
307 A complete list of options can be obtained by running
311 Below we discuss some of the more common options.
317 Installation prefix for C<isl>
319 =item C<--with-int=[gmp|imath]>
321 Select the integer library to be used by C<isl>, the default is C<gmp>.
322 Note that C<isl> may run significantly slower if you use C<imath>.
324 =item C<--with-gmp-prefix>
326 Installation prefix for C<GMP> (architecture-independent files).
328 =item C<--with-gmp-exec-prefix>
330 Installation prefix for C<GMP> (architecture-dependent files).
338 =item 4 Install (optional)
344 =head1 Integer Set Library
346 =head2 Initialization
348 All manipulations of integer sets and relations occur within
349 the context of an C<isl_ctx>.
350 A given C<isl_ctx> can only be used within a single thread.
351 All arguments of a function are required to have been allocated
352 within the same context.
353 There are currently no functions available for moving an object
354 from one C<isl_ctx> to another C<isl_ctx>. This means that
355 there is currently no way of safely moving an object from one
356 thread to another, unless the whole C<isl_ctx> is moved.
358 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
359 freed using C<isl_ctx_free>.
360 All objects allocated within an C<isl_ctx> should be freed
361 before the C<isl_ctx> itself is freed.
363 isl_ctx *isl_ctx_alloc();
364 void isl_ctx_free(isl_ctx *ctx);
366 The user can impose a bound on the number of low-level I<operations>
367 that can be performed by an C<isl_ctx>. This bound can be set and
368 retrieved using the following functions. A bound of zero means that
369 no bound is imposed. The number of operations performed can be
370 reset using C<isl_ctx_reset_operations>. Note that the number
371 of low-level operations needed to perform a high-level computation
372 may differ significantly across different versions
373 of C<isl>, but it should be the same across different platforms
374 for the same version of C<isl>.
376 Warning: This feature is experimental. C<isl> has good support to abort and
377 bail out during the computation, but this feature may exercise error code paths
378 that are normally not used that much. Consequently, it is not unlikely that
379 hidden bugs will be exposed.
381 void isl_ctx_set_max_operations(isl_ctx *ctx,
382 unsigned long max_operations);
383 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
384 void isl_ctx_reset_operations(isl_ctx *ctx);
386 =head2 Memory Management
388 Since a high-level operation on isl objects usually involves
389 several substeps and since the user is usually not interested in
390 the intermediate results, most functions that return a new object
391 will also release all the objects passed as arguments.
392 If the user still wants to use one or more of these arguments
393 after the function call, she should pass along a copy of the
394 object rather than the object itself.
395 The user is then responsible for making sure that the original
396 object gets used somewhere else or is explicitly freed.
398 The arguments and return values of all documented functions are
399 annotated to make clear which arguments are released and which
400 arguments are preserved. In particular, the following annotations
407 C<__isl_give> means that a new object is returned.
408 The user should make sure that the returned pointer is
409 used exactly once as a value for an C<__isl_take> argument.
410 In between, it can be used as a value for as many
411 C<__isl_keep> arguments as the user likes.
412 There is one exception, and that is the case where the
413 pointer returned is C<NULL>. Is this case, the user
414 is free to use it as an C<__isl_take> argument or not.
418 C<__isl_null> means that a C<NULL> value is returned.
422 C<__isl_take> means that the object the argument points to
423 is taken over by the function and may no longer be used
424 by the user as an argument to any other function.
425 The pointer value must be one returned by a function
426 returning an C<__isl_give> pointer.
427 If the user passes in a C<NULL> value, then this will
428 be treated as an error in the sense that the function will
429 not perform its usual operation. However, it will still
430 make sure that all the other C<__isl_take> arguments
435 C<__isl_keep> means that the function will only use the object
436 temporarily. After the function has finished, the user
437 can still use it as an argument to other functions.
438 A C<NULL> value will be treated in the same way as
439 a C<NULL> value for an C<__isl_take> argument.
445 An C<isl_val> represents an integer value, a rational value
446 or one of three special values, infinity, negative infinity and NaN.
447 Some predefined values can be created using the following functions.
450 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
451 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
452 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
453 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
454 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
455 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
457 Specific integer values can be created using the following functions.
460 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
462 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
464 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
465 size_t n, size_t size, const void *chunks);
467 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
468 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
469 The least significant digit is assumed to be stored first.
471 Value objects can be copied and freed using the following functions.
474 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
475 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
477 They can be inspected using the following functions.
480 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
481 long isl_val_get_num_si(__isl_keep isl_val *v);
482 long isl_val_get_den_si(__isl_keep isl_val *v);
483 double isl_val_get_d(__isl_keep isl_val *v);
484 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
486 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
487 size_t size, void *chunks);
489 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
490 of C<size> bytes needed to store the absolute value of the
492 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
493 which is assumed to have been preallocated by the caller.
494 The least significant digit is stored first.
495 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
496 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
497 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
499 An C<isl_val> can be modified using the following function.
502 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
505 The following unary properties are defined on C<isl_val>s.
508 int isl_val_sgn(__isl_keep isl_val *v);
509 int isl_val_is_zero(__isl_keep isl_val *v);
510 int isl_val_is_one(__isl_keep isl_val *v);
511 int isl_val_is_negone(__isl_keep isl_val *v);
512 int isl_val_is_nonneg(__isl_keep isl_val *v);
513 int isl_val_is_nonpos(__isl_keep isl_val *v);
514 int isl_val_is_pos(__isl_keep isl_val *v);
515 int isl_val_is_neg(__isl_keep isl_val *v);
516 int isl_val_is_int(__isl_keep isl_val *v);
517 int isl_val_is_rat(__isl_keep isl_val *v);
518 int isl_val_is_nan(__isl_keep isl_val *v);
519 int isl_val_is_infty(__isl_keep isl_val *v);
520 int isl_val_is_neginfty(__isl_keep isl_val *v);
522 Note that the sign of NaN is undefined.
524 The following binary properties are defined on pairs of C<isl_val>s.
527 int isl_val_lt(__isl_keep isl_val *v1,
528 __isl_keep isl_val *v2);
529 int isl_val_le(__isl_keep isl_val *v1,
530 __isl_keep isl_val *v2);
531 int isl_val_gt(__isl_keep isl_val *v1,
532 __isl_keep isl_val *v2);
533 int isl_val_ge(__isl_keep isl_val *v1,
534 __isl_keep isl_val *v2);
535 int isl_val_eq(__isl_keep isl_val *v1,
536 __isl_keep isl_val *v2);
537 int isl_val_ne(__isl_keep isl_val *v1,
538 __isl_keep isl_val *v2);
540 For integer C<isl_val>s we additionally have the following binary property.
543 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
544 __isl_keep isl_val *v2);
546 An C<isl_val> can also be compared to an integer using the following
547 function. The result is undefined for NaN.
550 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
552 The following unary operations are available on C<isl_val>s.
555 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
556 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
557 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
558 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
559 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
561 The following binary operations are available on C<isl_val>s.
564 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
565 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
566 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
567 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
568 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
569 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
570 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
571 __isl_take isl_val *v2);
572 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
573 __isl_take isl_val *v2);
574 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
575 __isl_take isl_val *v2);
576 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
578 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
579 __isl_take isl_val *v2);
580 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
582 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
583 __isl_take isl_val *v2);
584 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
586 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
587 __isl_take isl_val *v2);
589 On integer values, we additionally have the following operations.
592 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
593 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
594 __isl_take isl_val *v2);
595 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
596 __isl_take isl_val *v2);
597 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
598 __isl_take isl_val *v2, __isl_give isl_val **x,
599 __isl_give isl_val **y);
601 The function C<isl_val_gcdext> returns the greatest common divisor g
602 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
603 that C<*x> * C<v1> + C<*y> * C<v2> = g.
605 A value can be read from input using
608 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
611 A value can be printed using
614 __isl_give isl_printer *isl_printer_print_val(
615 __isl_take isl_printer *p, __isl_keep isl_val *v);
617 =head3 GMP specific functions
619 These functions are only available if C<isl> has been compiled with C<GMP>
622 Specific integer and rational values can be created from C<GMP> values using
623 the following functions.
625 #include <isl/val_gmp.h>
626 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
628 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
629 const mpz_t n, const mpz_t d);
631 The numerator and denominator of a rational value can be extracted as
632 C<GMP> values using the following functions.
634 #include <isl/val_gmp.h>
635 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
636 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
638 =head2 Sets and Relations
640 C<isl> uses six types of objects for representing sets and relations,
641 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
642 C<isl_union_set> and C<isl_union_map>.
643 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
644 can be described as a conjunction of affine constraints, while
645 C<isl_set> and C<isl_map> represent unions of
646 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
647 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
648 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
649 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
650 where spaces are considered different if they have a different number
651 of dimensions and/or different names (see L<"Spaces">).
652 The difference between sets and relations (maps) is that sets have
653 one set of variables, while relations have two sets of variables,
654 input variables and output variables.
656 =head2 Error Handling
658 C<isl> supports different ways to react in case a runtime error is triggered.
659 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
660 with two maps that have incompatible spaces. There are three possible ways
661 to react on error: to warn, to continue or to abort.
663 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
664 the last error in the corresponding C<isl_ctx> and the function in which the
665 error was triggered returns C<NULL>. An error does not corrupt internal state,
666 such that isl can continue to be used. C<isl> also provides functions to
667 read the last error and to reset the memory that stores the last error. The
668 last error is only stored for information purposes. Its presence does not
669 change the behavior of C<isl>. Hence, resetting an error is not required to
670 continue to use isl, but only to observe new errors.
673 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
674 void isl_ctx_reset_error(isl_ctx *ctx);
676 Another option is to continue on error. This is similar to warn on error mode,
677 except that C<isl> does not print any warning. This allows a program to
678 implement its own error reporting.
680 The last option is to directly abort the execution of the program from within
681 the isl library. This makes it obviously impossible to recover from an error,
682 but it allows to directly spot the error location. By aborting on error,
683 debuggers break at the location the error occurred and can provide a stack
684 trace. Other tools that automatically provide stack traces on abort or that do
685 not want to continue execution after an error was triggered may also prefer to
688 The on error behavior of isl can be specified by calling
689 C<isl_options_set_on_error> or by setting the command line option
690 C<--isl-on-error>. Valid arguments for the function call are
691 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
692 choices for the command line option are C<warn>, C<continue> and C<abort>.
693 It is also possible to query the current error mode.
695 #include <isl/options.h>
696 int isl_options_set_on_error(isl_ctx *ctx, int val);
697 int isl_options_get_on_error(isl_ctx *ctx);
701 Identifiers are used to identify both individual dimensions
702 and tuples of dimensions. They consist of an optional name and an optional
703 user pointer. The name and the user pointer cannot both be C<NULL>, however.
704 Identifiers with the same name but different pointer values
705 are considered to be distinct.
706 Similarly, identifiers with different names but the same pointer value
707 are also considered to be distinct.
708 Equal identifiers are represented using the same object.
709 Pairs of identifiers can therefore be tested for equality using the
711 Identifiers can be constructed, copied, freed, inspected and printed
712 using the following functions.
715 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
716 __isl_keep const char *name, void *user);
717 __isl_give isl_id *isl_id_set_free_user(
718 __isl_take isl_id *id,
719 __isl_give void (*free_user)(void *user));
720 __isl_give isl_id *isl_id_copy(isl_id *id);
721 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
723 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
724 void *isl_id_get_user(__isl_keep isl_id *id);
725 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
727 __isl_give isl_printer *isl_printer_print_id(
728 __isl_take isl_printer *p, __isl_keep isl_id *id);
730 The callback set by C<isl_id_set_free_user> is called on the user
731 pointer when the last reference to the C<isl_id> is freed.
732 Note that C<isl_id_get_name> returns a pointer to some internal
733 data structure, so the result can only be used while the
734 corresponding C<isl_id> is alive.
738 Whenever a new set, relation or similiar object is created from scratch,
739 the space in which it lives needs to be specified using an C<isl_space>.
740 Each space involves zero or more parameters and zero, one or two
741 tuples of set or input/output dimensions. The parameters and dimensions
742 are identified by an C<isl_dim_type> and a position.
743 The type C<isl_dim_param> refers to parameters,
744 the type C<isl_dim_set> refers to set dimensions (for spaces
745 with a single tuple of dimensions) and the types C<isl_dim_in>
746 and C<isl_dim_out> refer to input and output dimensions
747 (for spaces with two tuples of dimensions).
748 Local spaces (see L</"Local Spaces">) also contain dimensions
749 of type C<isl_dim_div>.
750 Note that parameters are only identified by their position within
751 a given object. Across different objects, parameters are (usually)
752 identified by their names or identifiers. Only unnamed parameters
753 are identified by their positions across objects. The use of unnamed
754 parameters is discouraged.
756 #include <isl/space.h>
757 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
758 unsigned nparam, unsigned n_in, unsigned n_out);
759 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
761 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
762 unsigned nparam, unsigned dim);
763 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
764 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
765 unsigned isl_space_dim(__isl_keep isl_space *space,
766 enum isl_dim_type type);
768 The space used for creating a parameter domain
769 needs to be created using C<isl_space_params_alloc>.
770 For other sets, the space
771 needs to be created using C<isl_space_set_alloc>, while
772 for a relation, the space
773 needs to be created using C<isl_space_alloc>.
774 C<isl_space_dim> can be used
775 to find out the number of dimensions of each type in
776 a space, where type may be
777 C<isl_dim_param>, C<isl_dim_in> (only for relations),
778 C<isl_dim_out> (only for relations), C<isl_dim_set>
779 (only for sets) or C<isl_dim_all>.
781 To check whether a given space is that of a set or a map
782 or whether it is a parameter space, use these functions:
784 #include <isl/space.h>
785 int isl_space_is_params(__isl_keep isl_space *space);
786 int isl_space_is_set(__isl_keep isl_space *space);
787 int isl_space_is_map(__isl_keep isl_space *space);
789 Spaces can be compared using the following functions:
791 #include <isl/space.h>
792 int isl_space_is_equal(__isl_keep isl_space *space1,
793 __isl_keep isl_space *space2);
794 int isl_space_is_domain(__isl_keep isl_space *space1,
795 __isl_keep isl_space *space2);
796 int isl_space_is_range(__isl_keep isl_space *space1,
797 __isl_keep isl_space *space2);
799 C<isl_space_is_domain> checks whether the first argument is equal
800 to the domain of the second argument. This requires in particular that
801 the first argument is a set space and that the second argument
804 It is often useful to create objects that live in the
805 same space as some other object. This can be accomplished
806 by creating the new objects
807 (see L</"Creating New Sets and Relations"> or
808 L</"Creating New (Piecewise) Quasipolynomials">) based on the space
809 of the original object.
812 __isl_give isl_space *isl_basic_set_get_space(
813 __isl_keep isl_basic_set *bset);
814 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
816 #include <isl/union_set.h>
817 __isl_give isl_space *isl_union_set_get_space(
818 __isl_keep isl_union_set *uset);
821 __isl_give isl_space *isl_basic_map_get_space(
822 __isl_keep isl_basic_map *bmap);
823 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
825 #include <isl/union_map.h>
826 __isl_give isl_space *isl_union_map_get_space(
827 __isl_keep isl_union_map *umap);
829 #include <isl/constraint.h>
830 __isl_give isl_space *isl_constraint_get_space(
831 __isl_keep isl_constraint *constraint);
833 #include <isl/polynomial.h>
834 __isl_give isl_space *isl_qpolynomial_get_domain_space(
835 __isl_keep isl_qpolynomial *qp);
836 __isl_give isl_space *isl_qpolynomial_get_space(
837 __isl_keep isl_qpolynomial *qp);
838 __isl_give isl_space *isl_qpolynomial_fold_get_space(
839 __isl_keep isl_qpolynomial_fold *fold);
840 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
841 __isl_keep isl_pw_qpolynomial *pwqp);
842 __isl_give isl_space *isl_pw_qpolynomial_get_space(
843 __isl_keep isl_pw_qpolynomial *pwqp);
844 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
845 __isl_keep isl_pw_qpolynomial_fold *pwf);
846 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
847 __isl_keep isl_pw_qpolynomial_fold *pwf);
848 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
849 __isl_keep isl_union_pw_qpolynomial *upwqp);
850 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
851 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
854 __isl_give isl_space *isl_multi_val_get_space(
855 __isl_keep isl_multi_val *mv);
858 __isl_give isl_space *isl_aff_get_domain_space(
859 __isl_keep isl_aff *aff);
860 __isl_give isl_space *isl_aff_get_space(
861 __isl_keep isl_aff *aff);
862 __isl_give isl_space *isl_pw_aff_get_domain_space(
863 __isl_keep isl_pw_aff *pwaff);
864 __isl_give isl_space *isl_pw_aff_get_space(
865 __isl_keep isl_pw_aff *pwaff);
866 __isl_give isl_space *isl_multi_aff_get_domain_space(
867 __isl_keep isl_multi_aff *maff);
868 __isl_give isl_space *isl_multi_aff_get_space(
869 __isl_keep isl_multi_aff *maff);
870 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
871 __isl_keep isl_pw_multi_aff *pma);
872 __isl_give isl_space *isl_pw_multi_aff_get_space(
873 __isl_keep isl_pw_multi_aff *pma);
874 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
875 __isl_keep isl_union_pw_multi_aff *upma);
876 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
877 __isl_keep isl_multi_pw_aff *mpa);
878 __isl_give isl_space *isl_multi_pw_aff_get_space(
879 __isl_keep isl_multi_pw_aff *mpa);
881 #include <isl/point.h>
882 __isl_give isl_space *isl_point_get_space(
883 __isl_keep isl_point *pnt);
885 The identifiers or names of the individual dimensions may be set or read off
886 using the following functions.
888 #include <isl/space.h>
889 __isl_give isl_space *isl_space_set_dim_id(
890 __isl_take isl_space *space,
891 enum isl_dim_type type, unsigned pos,
892 __isl_take isl_id *id);
893 int isl_space_has_dim_id(__isl_keep isl_space *space,
894 enum isl_dim_type type, unsigned pos);
895 __isl_give isl_id *isl_space_get_dim_id(
896 __isl_keep isl_space *space,
897 enum isl_dim_type type, unsigned pos);
898 __isl_give isl_space *isl_space_set_dim_name(
899 __isl_take isl_space *space,
900 enum isl_dim_type type, unsigned pos,
901 __isl_keep const char *name);
902 int isl_space_has_dim_name(__isl_keep isl_space *space,
903 enum isl_dim_type type, unsigned pos);
904 __isl_keep const char *isl_space_get_dim_name(
905 __isl_keep isl_space *space,
906 enum isl_dim_type type, unsigned pos);
908 Note that C<isl_space_get_name> returns a pointer to some internal
909 data structure, so the result can only be used while the
910 corresponding C<isl_space> is alive.
911 Also note that every function that operates on two sets or relations
912 requires that both arguments have the same parameters. This also
913 means that if one of the arguments has named parameters, then the
914 other needs to have named parameters too and the names need to match.
915 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
916 arguments may have different parameters (as long as they are named),
917 in which case the result will have as parameters the union of the parameters of
920 Given the identifier or name of a dimension (typically a parameter),
921 its position can be obtained from the following function.
923 #include <isl/space.h>
924 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
925 enum isl_dim_type type, __isl_keep isl_id *id);
926 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
927 enum isl_dim_type type, const char *name);
929 The identifiers or names of entire spaces may be set or read off
930 using the following functions.
932 #include <isl/space.h>
933 __isl_give isl_space *isl_space_set_tuple_id(
934 __isl_take isl_space *space,
935 enum isl_dim_type type, __isl_take isl_id *id);
936 __isl_give isl_space *isl_space_reset_tuple_id(
937 __isl_take isl_space *space, enum isl_dim_type type);
938 int isl_space_has_tuple_id(__isl_keep isl_space *space,
939 enum isl_dim_type type);
940 __isl_give isl_id *isl_space_get_tuple_id(
941 __isl_keep isl_space *space, enum isl_dim_type type);
942 __isl_give isl_space *isl_space_set_tuple_name(
943 __isl_take isl_space *space,
944 enum isl_dim_type type, const char *s);
945 int isl_space_has_tuple_name(__isl_keep isl_space *space,
946 enum isl_dim_type type);
947 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
948 enum isl_dim_type type);
950 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
951 or C<isl_dim_set>. As with C<isl_space_get_name>,
952 the C<isl_space_get_tuple_name> function returns a pointer to some internal
954 Binary operations require the corresponding spaces of their arguments
955 to have the same name.
957 To keep the names of all parameters and tuples, but reset the user pointers
958 of all the corresponding identifiers, use the following function.
960 __isl_give isl_space *isl_space_reset_user(
961 __isl_take isl_space *space);
963 Spaces can be nested. In particular, the domain of a set or
964 the domain or range of a relation can be a nested relation.
965 This process is also called I<wrapping>.
966 The functions for detecting, constructing and deconstructing
967 such nested spaces can be found in the wrapping properties
968 of L</"Unary Properties">, the wrapping operations
969 of L</"Unary Operations"> and the Cartesian product operations
970 of L</"Basic Operations">.
972 Spaces can be created from other spaces
973 using the following functions.
975 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
976 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
977 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
978 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
979 __isl_give isl_space *isl_space_domain_map(
980 __isl_take isl_space *space);
981 __isl_give isl_space *isl_space_range_map(
982 __isl_take isl_space *space);
983 __isl_give isl_space *isl_space_params(
984 __isl_take isl_space *space);
985 __isl_give isl_space *isl_space_set_from_params(
986 __isl_take isl_space *space);
987 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
988 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
989 __isl_take isl_space *right);
990 __isl_give isl_space *isl_space_align_params(
991 __isl_take isl_space *space1, __isl_take isl_space *space2)
992 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
993 enum isl_dim_type type, unsigned pos, unsigned n);
994 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
995 enum isl_dim_type type, unsigned n);
996 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
997 enum isl_dim_type type, unsigned first, unsigned n);
998 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
999 enum isl_dim_type dst_type, unsigned dst_pos,
1000 enum isl_dim_type src_type, unsigned src_pos,
1002 __isl_give isl_space *isl_space_map_from_set(
1003 __isl_take isl_space *space);
1004 __isl_give isl_space *isl_space_map_from_domain_and_range(
1005 __isl_take isl_space *domain,
1006 __isl_take isl_space *range);
1007 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1008 __isl_give isl_space *isl_space_curry(
1009 __isl_take isl_space *space);
1010 __isl_give isl_space *isl_space_uncurry(
1011 __isl_take isl_space *space);
1013 Note that if dimensions are added or removed from a space, then
1014 the name and the internal structure are lost.
1018 A local space is essentially a space with
1019 zero or more existentially quantified variables.
1020 The local space of a (constraint of a) basic set or relation can be obtained
1021 using the following functions.
1023 #include <isl/constraint.h>
1024 __isl_give isl_local_space *isl_constraint_get_local_space(
1025 __isl_keep isl_constraint *constraint);
1027 #include <isl/set.h>
1028 __isl_give isl_local_space *isl_basic_set_get_local_space(
1029 __isl_keep isl_basic_set *bset);
1031 #include <isl/map.h>
1032 __isl_give isl_local_space *isl_basic_map_get_local_space(
1033 __isl_keep isl_basic_map *bmap);
1035 A new local space can be created from a space using
1037 #include <isl/local_space.h>
1038 __isl_give isl_local_space *isl_local_space_from_space(
1039 __isl_take isl_space *space);
1041 They can be inspected, modified, copied and freed using the following functions.
1043 #include <isl/local_space.h>
1044 isl_ctx *isl_local_space_get_ctx(
1045 __isl_keep isl_local_space *ls);
1046 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1047 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1048 enum isl_dim_type type);
1049 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1050 __isl_take isl_local_space *ls,
1051 enum isl_dim_type type, __isl_take isl_id *id);
1052 int isl_local_space_has_dim_id(
1053 __isl_keep isl_local_space *ls,
1054 enum isl_dim_type type, unsigned pos);
1055 __isl_give isl_id *isl_local_space_get_dim_id(
1056 __isl_keep isl_local_space *ls,
1057 enum isl_dim_type type, unsigned pos);
1058 int isl_local_space_has_dim_name(
1059 __isl_keep isl_local_space *ls,
1060 enum isl_dim_type type, unsigned pos)
1061 const char *isl_local_space_get_dim_name(
1062 __isl_keep isl_local_space *ls,
1063 enum isl_dim_type type, unsigned pos);
1064 __isl_give isl_local_space *isl_local_space_set_dim_name(
1065 __isl_take isl_local_space *ls,
1066 enum isl_dim_type type, unsigned pos, const char *s);
1067 __isl_give isl_local_space *isl_local_space_set_dim_id(
1068 __isl_take isl_local_space *ls,
1069 enum isl_dim_type type, unsigned pos,
1070 __isl_take isl_id *id);
1071 __isl_give isl_space *isl_local_space_get_space(
1072 __isl_keep isl_local_space *ls);
1073 __isl_give isl_aff *isl_local_space_get_div(
1074 __isl_keep isl_local_space *ls, int pos);
1075 __isl_give isl_local_space *isl_local_space_copy(
1076 __isl_keep isl_local_space *ls);
1077 __isl_null isl_local_space *isl_local_space_free(
1078 __isl_take isl_local_space *ls);
1080 Note that C<isl_local_space_get_div> can only be used on local spaces
1083 Two local spaces can be compared using
1085 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1086 __isl_keep isl_local_space *ls2);
1088 Local spaces can be created from other local spaces
1089 using the functions described in L</"Unary Operations">
1090 and L</"Binary Operations">.
1092 =head2 Input and Output
1094 C<isl> supports its own input/output format, which is similar
1095 to the C<Omega> format, but also supports the C<PolyLib> format
1098 =head3 C<isl> format
1100 The C<isl> format is similar to that of C<Omega>, but has a different
1101 syntax for describing the parameters and allows for the definition
1102 of an existentially quantified variable as the integer division
1103 of an affine expression.
1104 For example, the set of integers C<i> between C<0> and C<n>
1105 such that C<i % 10 <= 6> can be described as
1107 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1110 A set or relation can have several disjuncts, separated
1111 by the keyword C<or>. Each disjunct is either a conjunction
1112 of constraints or a projection (C<exists>) of a conjunction
1113 of constraints. The constraints are separated by the keyword
1116 =head3 C<PolyLib> format
1118 If the represented set is a union, then the first line
1119 contains a single number representing the number of disjuncts.
1120 Otherwise, a line containing the number C<1> is optional.
1122 Each disjunct is represented by a matrix of constraints.
1123 The first line contains two numbers representing
1124 the number of rows and columns,
1125 where the number of rows is equal to the number of constraints
1126 and the number of columns is equal to two plus the number of variables.
1127 The following lines contain the actual rows of the constraint matrix.
1128 In each row, the first column indicates whether the constraint
1129 is an equality (C<0>) or inequality (C<1>). The final column
1130 corresponds to the constant term.
1132 If the set is parametric, then the coefficients of the parameters
1133 appear in the last columns before the constant column.
1134 The coefficients of any existentially quantified variables appear
1135 between those of the set variables and those of the parameters.
1137 =head3 Extended C<PolyLib> format
1139 The extended C<PolyLib> format is nearly identical to the
1140 C<PolyLib> format. The only difference is that the line
1141 containing the number of rows and columns of a constraint matrix
1142 also contains four additional numbers:
1143 the number of output dimensions, the number of input dimensions,
1144 the number of local dimensions (i.e., the number of existentially
1145 quantified variables) and the number of parameters.
1146 For sets, the number of ``output'' dimensions is equal
1147 to the number of set dimensions, while the number of ``input''
1152 #include <isl/set.h>
1153 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1154 isl_ctx *ctx, FILE *input);
1155 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1156 isl_ctx *ctx, const char *str);
1157 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1159 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1162 #include <isl/map.h>
1163 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1164 isl_ctx *ctx, FILE *input);
1165 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1166 isl_ctx *ctx, const char *str);
1167 __isl_give isl_map *isl_map_read_from_file(
1168 isl_ctx *ctx, FILE *input);
1169 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1172 #include <isl/union_set.h>
1173 __isl_give isl_union_set *isl_union_set_read_from_file(
1174 isl_ctx *ctx, FILE *input);
1175 __isl_give isl_union_set *isl_union_set_read_from_str(
1176 isl_ctx *ctx, const char *str);
1178 #include <isl/union_map.h>
1179 __isl_give isl_union_map *isl_union_map_read_from_file(
1180 isl_ctx *ctx, FILE *input);
1181 __isl_give isl_union_map *isl_union_map_read_from_str(
1182 isl_ctx *ctx, const char *str);
1184 The input format is autodetected and may be either the C<PolyLib> format
1185 or the C<isl> format.
1189 Before anything can be printed, an C<isl_printer> needs to
1192 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1194 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1195 __isl_null isl_printer *isl_printer_free(
1196 __isl_take isl_printer *printer);
1197 __isl_give char *isl_printer_get_str(
1198 __isl_keep isl_printer *printer);
1200 The printer can be inspected using the following functions.
1202 FILE *isl_printer_get_file(
1203 __isl_keep isl_printer *printer);
1204 int isl_printer_get_output_format(
1205 __isl_keep isl_printer *p);
1207 The behavior of the printer can be modified in various ways
1209 __isl_give isl_printer *isl_printer_set_output_format(
1210 __isl_take isl_printer *p, int output_format);
1211 __isl_give isl_printer *isl_printer_set_indent(
1212 __isl_take isl_printer *p, int indent);
1213 __isl_give isl_printer *isl_printer_set_indent_prefix(
1214 __isl_take isl_printer *p, const char *prefix);
1215 __isl_give isl_printer *isl_printer_indent(
1216 __isl_take isl_printer *p, int indent);
1217 __isl_give isl_printer *isl_printer_set_prefix(
1218 __isl_take isl_printer *p, const char *prefix);
1219 __isl_give isl_printer *isl_printer_set_suffix(
1220 __isl_take isl_printer *p, const char *suffix);
1222 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1223 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1224 and defaults to C<ISL_FORMAT_ISL>.
1225 Each line in the output is prefixed by C<indent_prefix>,
1226 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
1227 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1228 In the C<PolyLib> format output,
1229 the coefficients of the existentially quantified variables
1230 appear between those of the set variables and those
1232 The function C<isl_printer_indent> increases the indentation
1233 by the specified amount (which may be negative).
1235 To actually print something, use
1237 #include <isl/printer.h>
1238 __isl_give isl_printer *isl_printer_print_double(
1239 __isl_take isl_printer *p, double d);
1241 #include <isl/set.h>
1242 __isl_give isl_printer *isl_printer_print_basic_set(
1243 __isl_take isl_printer *printer,
1244 __isl_keep isl_basic_set *bset);
1245 __isl_give isl_printer *isl_printer_print_set(
1246 __isl_take isl_printer *printer,
1247 __isl_keep isl_set *set);
1249 #include <isl/map.h>
1250 __isl_give isl_printer *isl_printer_print_basic_map(
1251 __isl_take isl_printer *printer,
1252 __isl_keep isl_basic_map *bmap);
1253 __isl_give isl_printer *isl_printer_print_map(
1254 __isl_take isl_printer *printer,
1255 __isl_keep isl_map *map);
1257 #include <isl/union_set.h>
1258 __isl_give isl_printer *isl_printer_print_union_set(
1259 __isl_take isl_printer *p,
1260 __isl_keep isl_union_set *uset);
1262 #include <isl/union_map.h>
1263 __isl_give isl_printer *isl_printer_print_union_map(
1264 __isl_take isl_printer *p,
1265 __isl_keep isl_union_map *umap);
1267 When called on a file printer, the following function flushes
1268 the file. When called on a string printer, the buffer is cleared.
1270 __isl_give isl_printer *isl_printer_flush(
1271 __isl_take isl_printer *p);
1273 =head2 Creating New Sets and Relations
1275 C<isl> has functions for creating some standard sets and relations.
1279 =item * Empty sets and relations
1281 __isl_give isl_basic_set *isl_basic_set_empty(
1282 __isl_take isl_space *space);
1283 __isl_give isl_basic_map *isl_basic_map_empty(
1284 __isl_take isl_space *space);
1285 __isl_give isl_set *isl_set_empty(
1286 __isl_take isl_space *space);
1287 __isl_give isl_map *isl_map_empty(
1288 __isl_take isl_space *space);
1289 __isl_give isl_union_set *isl_union_set_empty(
1290 __isl_take isl_space *space);
1291 __isl_give isl_union_map *isl_union_map_empty(
1292 __isl_take isl_space *space);
1294 For C<isl_union_set>s and C<isl_union_map>s, the space
1295 is only used to specify the parameters.
1297 =item * Universe sets and relations
1299 __isl_give isl_basic_set *isl_basic_set_universe(
1300 __isl_take isl_space *space);
1301 __isl_give isl_basic_map *isl_basic_map_universe(
1302 __isl_take isl_space *space);
1303 __isl_give isl_set *isl_set_universe(
1304 __isl_take isl_space *space);
1305 __isl_give isl_map *isl_map_universe(
1306 __isl_take isl_space *space);
1307 __isl_give isl_union_set *isl_union_set_universe(
1308 __isl_take isl_union_set *uset);
1309 __isl_give isl_union_map *isl_union_map_universe(
1310 __isl_take isl_union_map *umap);
1312 The sets and relations constructed by the functions above
1313 contain all integer values, while those constructed by the
1314 functions below only contain non-negative values.
1316 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1317 __isl_take isl_space *space);
1318 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1319 __isl_take isl_space *space);
1320 __isl_give isl_set *isl_set_nat_universe(
1321 __isl_take isl_space *space);
1322 __isl_give isl_map *isl_map_nat_universe(
1323 __isl_take isl_space *space);
1325 =item * Identity relations
1327 __isl_give isl_basic_map *isl_basic_map_identity(
1328 __isl_take isl_space *space);
1329 __isl_give isl_map *isl_map_identity(
1330 __isl_take isl_space *space);
1332 The number of input and output dimensions in C<space> needs
1335 =item * Lexicographic order
1337 __isl_give isl_map *isl_map_lex_lt(
1338 __isl_take isl_space *set_space);
1339 __isl_give isl_map *isl_map_lex_le(
1340 __isl_take isl_space *set_space);
1341 __isl_give isl_map *isl_map_lex_gt(
1342 __isl_take isl_space *set_space);
1343 __isl_give isl_map *isl_map_lex_ge(
1344 __isl_take isl_space *set_space);
1345 __isl_give isl_map *isl_map_lex_lt_first(
1346 __isl_take isl_space *space, unsigned n);
1347 __isl_give isl_map *isl_map_lex_le_first(
1348 __isl_take isl_space *space, unsigned n);
1349 __isl_give isl_map *isl_map_lex_gt_first(
1350 __isl_take isl_space *space, unsigned n);
1351 __isl_give isl_map *isl_map_lex_ge_first(
1352 __isl_take isl_space *space, unsigned n);
1354 The first four functions take a space for a B<set>
1355 and return relations that express that the elements in the domain
1356 are lexicographically less
1357 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1358 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1359 than the elements in the range.
1360 The last four functions take a space for a map
1361 and return relations that express that the first C<n> dimensions
1362 in the domain are lexicographically less
1363 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1364 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1365 than the first C<n> dimensions in the range.
1369 A basic set or relation can be converted to a set or relation
1370 using the following functions.
1372 __isl_give isl_set *isl_set_from_basic_set(
1373 __isl_take isl_basic_set *bset);
1374 __isl_give isl_map *isl_map_from_basic_map(
1375 __isl_take isl_basic_map *bmap);
1377 Sets and relations can be converted to union sets and relations
1378 using the following functions.
1380 __isl_give isl_union_set *isl_union_set_from_basic_set(
1381 __isl_take isl_basic_set *bset);
1382 __isl_give isl_union_map *isl_union_map_from_basic_map(
1383 __isl_take isl_basic_map *bmap);
1384 __isl_give isl_union_set *isl_union_set_from_set(
1385 __isl_take isl_set *set);
1386 __isl_give isl_union_map *isl_union_map_from_map(
1387 __isl_take isl_map *map);
1389 The inverse conversions below can only be used if the input
1390 union set or relation is known to contain elements in exactly one
1393 __isl_give isl_set *isl_set_from_union_set(
1394 __isl_take isl_union_set *uset);
1395 __isl_give isl_map *isl_map_from_union_map(
1396 __isl_take isl_union_map *umap);
1398 A zero-dimensional (basic) set can be constructed on a given parameter domain
1399 using the following function.
1401 __isl_give isl_basic_set *isl_basic_set_from_params(
1402 __isl_take isl_basic_set *bset);
1403 __isl_give isl_set *isl_set_from_params(
1404 __isl_take isl_set *set);
1406 Sets and relations can be copied and freed again using the following
1409 __isl_give isl_basic_set *isl_basic_set_copy(
1410 __isl_keep isl_basic_set *bset);
1411 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1412 __isl_give isl_union_set *isl_union_set_copy(
1413 __isl_keep isl_union_set *uset);
1414 __isl_give isl_basic_map *isl_basic_map_copy(
1415 __isl_keep isl_basic_map *bmap);
1416 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1417 __isl_give isl_union_map *isl_union_map_copy(
1418 __isl_keep isl_union_map *umap);
1419 __isl_null isl_basic_set *isl_basic_set_free(
1420 __isl_take isl_basic_set *bset);
1421 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1422 __isl_null isl_union_set *isl_union_set_free(
1423 __isl_take isl_union_set *uset);
1424 __isl_null isl_basic_map *isl_basic_map_free(
1425 __isl_take isl_basic_map *bmap);
1426 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1427 __isl_null isl_union_map *isl_union_map_free(
1428 __isl_take isl_union_map *umap);
1430 Other sets and relations can be constructed by starting
1431 from a universe set or relation, adding equality and/or
1432 inequality constraints and then projecting out the
1433 existentially quantified variables, if any.
1434 Constraints can be constructed, manipulated and
1435 added to (or removed from) (basic) sets and relations
1436 using the following functions.
1438 #include <isl/constraint.h>
1439 __isl_give isl_constraint *isl_equality_alloc(
1440 __isl_take isl_local_space *ls);
1441 __isl_give isl_constraint *isl_inequality_alloc(
1442 __isl_take isl_local_space *ls);
1443 __isl_give isl_constraint *isl_constraint_set_constant_si(
1444 __isl_take isl_constraint *constraint, int v);
1445 __isl_give isl_constraint *isl_constraint_set_constant_val(
1446 __isl_take isl_constraint *constraint,
1447 __isl_take isl_val *v);
1448 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1449 __isl_take isl_constraint *constraint,
1450 enum isl_dim_type type, int pos, int v);
1451 __isl_give isl_constraint *
1452 isl_constraint_set_coefficient_val(
1453 __isl_take isl_constraint *constraint,
1454 enum isl_dim_type type, int pos,
1455 __isl_take isl_val *v);
1456 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1457 __isl_take isl_basic_map *bmap,
1458 __isl_take isl_constraint *constraint);
1459 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1460 __isl_take isl_basic_set *bset,
1461 __isl_take isl_constraint *constraint);
1462 __isl_give isl_map *isl_map_add_constraint(
1463 __isl_take isl_map *map,
1464 __isl_take isl_constraint *constraint);
1465 __isl_give isl_set *isl_set_add_constraint(
1466 __isl_take isl_set *set,
1467 __isl_take isl_constraint *constraint);
1468 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1469 __isl_take isl_basic_set *bset,
1470 __isl_take isl_constraint *constraint);
1472 For example, to create a set containing the even integers
1473 between 10 and 42, you would use the following code.
1476 isl_local_space *ls;
1478 isl_basic_set *bset;
1480 space = isl_space_set_alloc(ctx, 0, 2);
1481 bset = isl_basic_set_universe(isl_space_copy(space));
1482 ls = isl_local_space_from_space(space);
1484 c = isl_equality_alloc(isl_local_space_copy(ls));
1485 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1486 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1487 bset = isl_basic_set_add_constraint(bset, c);
1489 c = isl_inequality_alloc(isl_local_space_copy(ls));
1490 c = isl_constraint_set_constant_si(c, -10);
1491 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1492 bset = isl_basic_set_add_constraint(bset, c);
1494 c = isl_inequality_alloc(ls);
1495 c = isl_constraint_set_constant_si(c, 42);
1496 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1497 bset = isl_basic_set_add_constraint(bset, c);
1499 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1503 isl_basic_set *bset;
1504 bset = isl_basic_set_read_from_str(ctx,
1505 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1507 A basic set or relation can also be constructed from two matrices
1508 describing the equalities and the inequalities.
1510 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1511 __isl_take isl_space *space,
1512 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1513 enum isl_dim_type c1,
1514 enum isl_dim_type c2, enum isl_dim_type c3,
1515 enum isl_dim_type c4);
1516 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1517 __isl_take isl_space *space,
1518 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1519 enum isl_dim_type c1,
1520 enum isl_dim_type c2, enum isl_dim_type c3,
1521 enum isl_dim_type c4, enum isl_dim_type c5);
1523 The C<isl_dim_type> arguments indicate the order in which
1524 different kinds of variables appear in the input matrices
1525 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1526 C<isl_dim_set> and C<isl_dim_div> for sets and
1527 of C<isl_dim_cst>, C<isl_dim_param>,
1528 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1530 A (basic or union) set or relation can also be constructed from a
1531 (union) (piecewise) (multiple) affine expression
1532 or a list of affine expressions
1533 (See L<"Piecewise Quasi Affine Expressions"> and
1534 L<"Piecewise Multiple Quasi Affine Expressions">).
1536 __isl_give isl_basic_map *isl_basic_map_from_aff(
1537 __isl_take isl_aff *aff);
1538 __isl_give isl_map *isl_map_from_aff(
1539 __isl_take isl_aff *aff);
1540 __isl_give isl_set *isl_set_from_pw_aff(
1541 __isl_take isl_pw_aff *pwaff);
1542 __isl_give isl_map *isl_map_from_pw_aff(
1543 __isl_take isl_pw_aff *pwaff);
1544 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1545 __isl_take isl_space *domain_space,
1546 __isl_take isl_aff_list *list);
1547 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1548 __isl_take isl_multi_aff *maff)
1549 __isl_give isl_map *isl_map_from_multi_aff(
1550 __isl_take isl_multi_aff *maff)
1551 __isl_give isl_set *isl_set_from_pw_multi_aff(
1552 __isl_take isl_pw_multi_aff *pma);
1553 __isl_give isl_map *isl_map_from_pw_multi_aff(
1554 __isl_take isl_pw_multi_aff *pma);
1555 __isl_give isl_set *isl_set_from_multi_pw_aff(
1556 __isl_take isl_multi_pw_aff *mpa);
1557 __isl_give isl_map *isl_map_from_multi_pw_aff(
1558 __isl_take isl_multi_pw_aff *mpa);
1559 __isl_give isl_union_map *
1560 isl_union_map_from_union_pw_multi_aff(
1561 __isl_take isl_union_pw_multi_aff *upma);
1563 The C<domain_space> argument describes the domain of the resulting
1564 basic relation. It is required because the C<list> may consist
1565 of zero affine expressions.
1567 =head2 Inspecting Sets and Relations
1569 Usually, the user should not have to care about the actual constraints
1570 of the sets and maps, but should instead apply the abstract operations
1571 explained in the following sections.
1572 Occasionally, however, it may be required to inspect the individual
1573 coefficients of the constraints. This section explains how to do so.
1574 In these cases, it may also be useful to have C<isl> compute
1575 an explicit representation of the existentially quantified variables.
1577 __isl_give isl_set *isl_set_compute_divs(
1578 __isl_take isl_set *set);
1579 __isl_give isl_map *isl_map_compute_divs(
1580 __isl_take isl_map *map);
1581 __isl_give isl_union_set *isl_union_set_compute_divs(
1582 __isl_take isl_union_set *uset);
1583 __isl_give isl_union_map *isl_union_map_compute_divs(
1584 __isl_take isl_union_map *umap);
1586 This explicit representation defines the existentially quantified
1587 variables as integer divisions of the other variables, possibly
1588 including earlier existentially quantified variables.
1589 An explicitly represented existentially quantified variable therefore
1590 has a unique value when the values of the other variables are known.
1591 If, furthermore, the same existentials, i.e., existentials
1592 with the same explicit representations, should appear in the
1593 same order in each of the disjuncts of a set or map, then the user should call
1594 either of the following functions.
1596 __isl_give isl_set *isl_set_align_divs(
1597 __isl_take isl_set *set);
1598 __isl_give isl_map *isl_map_align_divs(
1599 __isl_take isl_map *map);
1601 Alternatively, the existentially quantified variables can be removed
1602 using the following functions, which compute an overapproximation.
1604 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1605 __isl_take isl_basic_set *bset);
1606 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1607 __isl_take isl_basic_map *bmap);
1608 __isl_give isl_set *isl_set_remove_divs(
1609 __isl_take isl_set *set);
1610 __isl_give isl_map *isl_map_remove_divs(
1611 __isl_take isl_map *map);
1613 It is also possible to only remove those divs that are defined
1614 in terms of a given range of dimensions or only those for which
1615 no explicit representation is known.
1617 __isl_give isl_basic_set *
1618 isl_basic_set_remove_divs_involving_dims(
1619 __isl_take isl_basic_set *bset,
1620 enum isl_dim_type type,
1621 unsigned first, unsigned n);
1622 __isl_give isl_basic_map *
1623 isl_basic_map_remove_divs_involving_dims(
1624 __isl_take isl_basic_map *bmap,
1625 enum isl_dim_type type,
1626 unsigned first, unsigned n);
1627 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1628 __isl_take isl_set *set, enum isl_dim_type type,
1629 unsigned first, unsigned n);
1630 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1631 __isl_take isl_map *map, enum isl_dim_type type,
1632 unsigned first, unsigned n);
1634 __isl_give isl_basic_set *
1635 isl_basic_set_remove_unknown_divs(
1636 __isl_take isl_basic_set *bset);
1637 __isl_give isl_set *isl_set_remove_unknown_divs(
1638 __isl_take isl_set *set);
1639 __isl_give isl_map *isl_map_remove_unknown_divs(
1640 __isl_take isl_map *map);
1642 To iterate over all the sets or maps in a union set or map, use
1644 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1645 int (*fn)(__isl_take isl_set *set, void *user),
1647 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1648 int (*fn)(__isl_take isl_map *map, void *user),
1651 The number of sets or maps in a union set or map can be obtained
1654 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1655 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1657 To extract the set or map in a given space from a union, use
1659 __isl_give isl_set *isl_union_set_extract_set(
1660 __isl_keep isl_union_set *uset,
1661 __isl_take isl_space *space);
1662 __isl_give isl_map *isl_union_map_extract_map(
1663 __isl_keep isl_union_map *umap,
1664 __isl_take isl_space *space);
1666 To iterate over all the basic sets or maps in a set or map, use
1668 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1669 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1671 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1672 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1675 The callback function C<fn> should return 0 if successful and
1676 -1 if an error occurs. In the latter case, or if any other error
1677 occurs, the above functions will return -1.
1679 It should be noted that C<isl> does not guarantee that
1680 the basic sets or maps passed to C<fn> are disjoint.
1681 If this is required, then the user should call one of
1682 the following functions first.
1684 __isl_give isl_set *isl_set_make_disjoint(
1685 __isl_take isl_set *set);
1686 __isl_give isl_map *isl_map_make_disjoint(
1687 __isl_take isl_map *map);
1689 The number of basic sets in a set can be obtained
1692 int isl_set_n_basic_set(__isl_keep isl_set *set);
1694 To iterate over the constraints of a basic set or map, use
1696 #include <isl/constraint.h>
1698 int isl_basic_set_n_constraint(
1699 __isl_keep isl_basic_set *bset);
1700 int isl_basic_set_foreach_constraint(
1701 __isl_keep isl_basic_set *bset,
1702 int (*fn)(__isl_take isl_constraint *c, void *user),
1704 int isl_basic_map_n_constraint(
1705 __isl_keep isl_basic_map *bmap);
1706 int isl_basic_map_foreach_constraint(
1707 __isl_keep isl_basic_map *bmap,
1708 int (*fn)(__isl_take isl_constraint *c, void *user),
1710 __isl_null isl_constraint *isl_constraint_free(
1711 __isl_take isl_constraint *c);
1713 Again, the callback function C<fn> should return 0 if successful and
1714 -1 if an error occurs. In the latter case, or if any other error
1715 occurs, the above functions will return -1.
1716 The constraint C<c> represents either an equality or an inequality.
1717 Use the following function to find out whether a constraint
1718 represents an equality. If not, it represents an inequality.
1720 int isl_constraint_is_equality(
1721 __isl_keep isl_constraint *constraint);
1723 It is also possible to obtain a list of constraints from a basic
1726 #include <isl/constraint.h>
1727 __isl_give isl_constraint_list *
1728 isl_basic_map_get_constraint_list(
1729 __isl_keep isl_basic_map *bmap);
1730 __isl_give isl_constraint_list *
1731 isl_basic_set_get_constraint_list(
1732 __isl_keep isl_basic_set *bset);
1734 These functions require that all existentially quantified variables
1735 have an explicit representation.
1736 The returned list can be manipulated using the functions in L<"Lists">.
1738 The coefficients of the constraints can be inspected using
1739 the following functions.
1741 int isl_constraint_is_lower_bound(
1742 __isl_keep isl_constraint *constraint,
1743 enum isl_dim_type type, unsigned pos);
1744 int isl_constraint_is_upper_bound(
1745 __isl_keep isl_constraint *constraint,
1746 enum isl_dim_type type, unsigned pos);
1747 __isl_give isl_val *isl_constraint_get_constant_val(
1748 __isl_keep isl_constraint *constraint);
1749 __isl_give isl_val *isl_constraint_get_coefficient_val(
1750 __isl_keep isl_constraint *constraint,
1751 enum isl_dim_type type, int pos);
1752 int isl_constraint_involves_dims(
1753 __isl_keep isl_constraint *constraint,
1754 enum isl_dim_type type, unsigned first, unsigned n);
1756 The explicit representations of the existentially quantified
1757 variables can be inspected using the following function.
1758 Note that the user is only allowed to use this function
1759 if the inspected set or map is the result of a call
1760 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1761 The existentially quantified variable is equal to the floor
1762 of the returned affine expression. The affine expression
1763 itself can be inspected using the functions in
1764 L<"Piecewise Quasi Affine Expressions">.
1766 __isl_give isl_aff *isl_constraint_get_div(
1767 __isl_keep isl_constraint *constraint, int pos);
1769 To obtain the constraints of a basic set or map in matrix
1770 form, use the following functions.
1772 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1773 __isl_keep isl_basic_set *bset,
1774 enum isl_dim_type c1, enum isl_dim_type c2,
1775 enum isl_dim_type c3, enum isl_dim_type c4);
1776 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1777 __isl_keep isl_basic_set *bset,
1778 enum isl_dim_type c1, enum isl_dim_type c2,
1779 enum isl_dim_type c3, enum isl_dim_type c4);
1780 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1781 __isl_keep isl_basic_map *bmap,
1782 enum isl_dim_type c1,
1783 enum isl_dim_type c2, enum isl_dim_type c3,
1784 enum isl_dim_type c4, enum isl_dim_type c5);
1785 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1786 __isl_keep isl_basic_map *bmap,
1787 enum isl_dim_type c1,
1788 enum isl_dim_type c2, enum isl_dim_type c3,
1789 enum isl_dim_type c4, enum isl_dim_type c5);
1791 The C<isl_dim_type> arguments dictate the order in which
1792 different kinds of variables appear in the resulting matrix
1793 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1794 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1796 The number of parameters, input, output or set dimensions can
1797 be obtained using the following functions.
1799 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1800 enum isl_dim_type type);
1801 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1802 enum isl_dim_type type);
1803 unsigned isl_set_dim(__isl_keep isl_set *set,
1804 enum isl_dim_type type);
1805 unsigned isl_map_dim(__isl_keep isl_map *map,
1806 enum isl_dim_type type);
1807 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1808 enum isl_dim_type type);
1810 Note that a C<isl_union_map> only has parameters.
1812 To check whether the description of a set or relation depends
1813 on one or more given dimensions, it is not necessary to iterate over all
1814 constraints. Instead the following functions can be used.
1816 int isl_basic_set_involves_dims(
1817 __isl_keep isl_basic_set *bset,
1818 enum isl_dim_type type, unsigned first, unsigned n);
1819 int isl_set_involves_dims(__isl_keep isl_set *set,
1820 enum isl_dim_type type, unsigned first, unsigned n);
1821 int isl_basic_map_involves_dims(
1822 __isl_keep isl_basic_map *bmap,
1823 enum isl_dim_type type, unsigned first, unsigned n);
1824 int isl_map_involves_dims(__isl_keep isl_map *map,
1825 enum isl_dim_type type, unsigned first, unsigned n);
1827 Similarly, the following functions can be used to check whether
1828 a given dimension is involved in any lower or upper bound.
1830 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1831 enum isl_dim_type type, unsigned pos);
1832 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1833 enum isl_dim_type type, unsigned pos);
1835 Note that these functions return true even if there is a bound on
1836 the dimension on only some of the basic sets of C<set>.
1837 To check if they have a bound for all of the basic sets in C<set>,
1838 use the following functions instead.
1840 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1841 enum isl_dim_type type, unsigned pos);
1842 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1843 enum isl_dim_type type, unsigned pos);
1845 The identifiers or names of the domain and range spaces of a set
1846 or relation can be read off or set using the following functions.
1848 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1849 __isl_take isl_basic_set *bset,
1850 __isl_take isl_id *id);
1851 __isl_give isl_set *isl_set_set_tuple_id(
1852 __isl_take isl_set *set, __isl_take isl_id *id);
1853 __isl_give isl_set *isl_set_reset_tuple_id(
1854 __isl_take isl_set *set);
1855 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1856 __isl_give isl_id *isl_set_get_tuple_id(
1857 __isl_keep isl_set *set);
1858 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1859 __isl_take isl_basic_map *bmap,
1860 enum isl_dim_type type, __isl_take isl_id *id);
1861 __isl_give isl_map *isl_map_set_tuple_id(
1862 __isl_take isl_map *map, enum isl_dim_type type,
1863 __isl_take isl_id *id);
1864 __isl_give isl_map *isl_map_reset_tuple_id(
1865 __isl_take isl_map *map, enum isl_dim_type type);
1866 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1867 enum isl_dim_type type);
1868 __isl_give isl_id *isl_map_get_tuple_id(
1869 __isl_keep isl_map *map, enum isl_dim_type type);
1871 const char *isl_basic_set_get_tuple_name(
1872 __isl_keep isl_basic_set *bset);
1873 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1874 __isl_take isl_basic_set *set, const char *s);
1875 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1876 const char *isl_set_get_tuple_name(
1877 __isl_keep isl_set *set);
1878 __isl_give isl_set *isl_set_set_tuple_name(
1879 __isl_take isl_set *set, const char *s);
1880 const char *isl_basic_map_get_tuple_name(
1881 __isl_keep isl_basic_map *bmap,
1882 enum isl_dim_type type);
1883 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1884 __isl_take isl_basic_map *bmap,
1885 enum isl_dim_type type, const char *s);
1886 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1887 enum isl_dim_type type);
1888 const char *isl_map_get_tuple_name(
1889 __isl_keep isl_map *map,
1890 enum isl_dim_type type);
1891 __isl_give isl_map *isl_map_set_tuple_name(
1892 __isl_take isl_map *map,
1893 enum isl_dim_type type, const char *s);
1895 As with C<isl_space_get_tuple_name>, the value returned points to
1896 an internal data structure.
1897 The identifiers, positions or names of individual dimensions can be
1898 read off using the following functions.
1900 __isl_give isl_id *isl_basic_set_get_dim_id(
1901 __isl_keep isl_basic_set *bset,
1902 enum isl_dim_type type, unsigned pos);
1903 __isl_give isl_set *isl_set_set_dim_id(
1904 __isl_take isl_set *set, enum isl_dim_type type,
1905 unsigned pos, __isl_take isl_id *id);
1906 int isl_set_has_dim_id(__isl_keep isl_set *set,
1907 enum isl_dim_type type, unsigned pos);
1908 __isl_give isl_id *isl_set_get_dim_id(
1909 __isl_keep isl_set *set, enum isl_dim_type type,
1911 int isl_basic_map_has_dim_id(
1912 __isl_keep isl_basic_map *bmap,
1913 enum isl_dim_type type, unsigned pos);
1914 __isl_give isl_map *isl_map_set_dim_id(
1915 __isl_take isl_map *map, enum isl_dim_type type,
1916 unsigned pos, __isl_take isl_id *id);
1917 int isl_map_has_dim_id(__isl_keep isl_map *map,
1918 enum isl_dim_type type, unsigned pos);
1919 __isl_give isl_id *isl_map_get_dim_id(
1920 __isl_keep isl_map *map, enum isl_dim_type type,
1922 __isl_give isl_id *isl_union_map_get_dim_id(
1923 __isl_keep isl_union_map *umap,
1924 enum isl_dim_type type, unsigned pos);
1926 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1927 enum isl_dim_type type, __isl_keep isl_id *id);
1928 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1929 enum isl_dim_type type, __isl_keep isl_id *id);
1930 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1931 enum isl_dim_type type, const char *name);
1932 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1933 enum isl_dim_type type, const char *name);
1935 const char *isl_constraint_get_dim_name(
1936 __isl_keep isl_constraint *constraint,
1937 enum isl_dim_type type, unsigned pos);
1938 const char *isl_basic_set_get_dim_name(
1939 __isl_keep isl_basic_set *bset,
1940 enum isl_dim_type type, unsigned pos);
1941 int isl_set_has_dim_name(__isl_keep isl_set *set,
1942 enum isl_dim_type type, unsigned pos);
1943 const char *isl_set_get_dim_name(
1944 __isl_keep isl_set *set,
1945 enum isl_dim_type type, unsigned pos);
1946 const char *isl_basic_map_get_dim_name(
1947 __isl_keep isl_basic_map *bmap,
1948 enum isl_dim_type type, unsigned pos);
1949 int isl_map_has_dim_name(__isl_keep isl_map *map,
1950 enum isl_dim_type type, unsigned pos);
1951 const char *isl_map_get_dim_name(
1952 __isl_keep isl_map *map,
1953 enum isl_dim_type type, unsigned pos);
1955 These functions are mostly useful to obtain the identifiers, positions
1956 or names of the parameters. Identifiers of individual dimensions are
1957 essentially only useful for printing. They are ignored by all other
1958 operations and may not be preserved across those operations.
1960 The user pointers on all parameters and tuples can be reset
1961 using the following functions.
1963 #include <isl/set.h>
1964 __isl_give isl_set *isl_set_reset_user(
1965 __isl_take isl_set *set);
1966 #include <isl/map.h>
1967 __isl_give isl_map *isl_map_reset_user(
1968 __isl_take isl_map *map);
1969 #include <isl/union_set.h>
1970 __isl_give isl_union_set *isl_union_set_reset_user(
1971 __isl_take isl_union_set *uset);
1972 #include <isl/union_map.h>
1973 __isl_give isl_union_map *isl_union_map_reset_user(
1974 __isl_take isl_union_map *umap);
1978 =head3 Unary Properties
1984 The following functions test whether the given set or relation
1985 contains any integer points. The ``plain'' variants do not perform
1986 any computations, but simply check if the given set or relation
1987 is already known to be empty.
1989 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1990 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1991 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1992 int isl_set_is_empty(__isl_keep isl_set *set);
1993 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1994 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1995 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1996 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1997 int isl_map_is_empty(__isl_keep isl_map *map);
1998 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2000 =item * Universality
2002 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2003 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2004 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2006 =item * Single-valuedness
2008 int isl_basic_map_is_single_valued(
2009 __isl_keep isl_basic_map *bmap);
2010 int isl_map_plain_is_single_valued(
2011 __isl_keep isl_map *map);
2012 int isl_map_is_single_valued(__isl_keep isl_map *map);
2013 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2017 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2018 int isl_map_is_injective(__isl_keep isl_map *map);
2019 int isl_union_map_plain_is_injective(
2020 __isl_keep isl_union_map *umap);
2021 int isl_union_map_is_injective(
2022 __isl_keep isl_union_map *umap);
2026 int isl_map_is_bijective(__isl_keep isl_map *map);
2027 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2031 __isl_give isl_val *
2032 isl_basic_map_plain_get_val_if_fixed(
2033 __isl_keep isl_basic_map *bmap,
2034 enum isl_dim_type type, unsigned pos);
2035 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2036 __isl_keep isl_set *set,
2037 enum isl_dim_type type, unsigned pos);
2038 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2039 __isl_keep isl_map *map,
2040 enum isl_dim_type type, unsigned pos);
2042 If the set or relation obviously lies on a hyperplane where the given dimension
2043 has a fixed value, then return that value.
2044 Otherwise return NaN.
2048 int isl_set_dim_residue_class_val(
2049 __isl_keep isl_set *set,
2050 int pos, __isl_give isl_val **modulo,
2051 __isl_give isl_val **residue);
2053 Check if the values of the given set dimension are equal to a fixed
2054 value modulo some integer value. If so, assign the modulo to C<*modulo>
2055 and the fixed value to C<*residue>. If the given dimension attains only
2056 a single value, then assign C<0> to C<*modulo> and the fixed value to
2058 If the dimension does not attain only a single value and if no modulo
2059 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2063 To check whether a set is a parameter domain, use this function:
2065 int isl_set_is_params(__isl_keep isl_set *set);
2066 int isl_union_set_is_params(
2067 __isl_keep isl_union_set *uset);
2071 The following functions check whether the space of the given
2072 (basic) set or relation range is a wrapped relation.
2074 #include <isl/space.h>
2075 int isl_space_is_wrapping(
2076 __isl_keep isl_space *space);
2077 int isl_space_domain_is_wrapping(
2078 __isl_keep isl_space *space);
2079 int isl_space_range_is_wrapping(
2080 __isl_keep isl_space *space);
2082 #include <isl/set.h>
2083 int isl_basic_set_is_wrapping(
2084 __isl_keep isl_basic_set *bset);
2085 int isl_set_is_wrapping(__isl_keep isl_set *set);
2087 #include <isl/map.h>
2088 int isl_map_domain_is_wrapping(
2089 __isl_keep isl_map *map);
2090 int isl_map_range_is_wrapping(
2091 __isl_keep isl_map *map);
2093 The input to C<isl_space_is_wrapping> should
2094 be the space of a set, while that of
2095 C<isl_space_domain_is_wrapping> and
2096 C<isl_space_range_is_wrapping> should be the space of a relation.
2098 =item * Internal Product
2100 int isl_basic_map_can_zip(
2101 __isl_keep isl_basic_map *bmap);
2102 int isl_map_can_zip(__isl_keep isl_map *map);
2104 Check whether the product of domain and range of the given relation
2106 i.e., whether both domain and range are nested relations.
2110 int isl_basic_map_can_curry(
2111 __isl_keep isl_basic_map *bmap);
2112 int isl_map_can_curry(__isl_keep isl_map *map);
2114 Check whether the domain of the (basic) relation is a wrapped relation.
2116 int isl_basic_map_can_uncurry(
2117 __isl_keep isl_basic_map *bmap);
2118 int isl_map_can_uncurry(__isl_keep isl_map *map);
2120 Check whether the range of the (basic) relation is a wrapped relation.
2124 =head3 Binary Properties
2130 int isl_basic_set_plain_is_equal(
2131 __isl_keep isl_basic_set *bset1,
2132 __isl_keep isl_basic_set *bset2);
2133 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2134 __isl_keep isl_set *set2);
2135 int isl_set_is_equal(__isl_keep isl_set *set1,
2136 __isl_keep isl_set *set2);
2137 int isl_union_set_is_equal(
2138 __isl_keep isl_union_set *uset1,
2139 __isl_keep isl_union_set *uset2);
2140 int isl_basic_map_is_equal(
2141 __isl_keep isl_basic_map *bmap1,
2142 __isl_keep isl_basic_map *bmap2);
2143 int isl_map_is_equal(__isl_keep isl_map *map1,
2144 __isl_keep isl_map *map2);
2145 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2146 __isl_keep isl_map *map2);
2147 int isl_union_map_is_equal(
2148 __isl_keep isl_union_map *umap1,
2149 __isl_keep isl_union_map *umap2);
2151 =item * Disjointness
2153 int isl_basic_set_is_disjoint(
2154 __isl_keep isl_basic_set *bset1,
2155 __isl_keep isl_basic_set *bset2);
2156 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2157 __isl_keep isl_set *set2);
2158 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2159 __isl_keep isl_set *set2);
2160 int isl_basic_map_is_disjoint(
2161 __isl_keep isl_basic_map *bmap1,
2162 __isl_keep isl_basic_map *bmap2);
2163 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2164 __isl_keep isl_map *map2);
2168 int isl_basic_set_is_subset(
2169 __isl_keep isl_basic_set *bset1,
2170 __isl_keep isl_basic_set *bset2);
2171 int isl_set_is_subset(__isl_keep isl_set *set1,
2172 __isl_keep isl_set *set2);
2173 int isl_set_is_strict_subset(
2174 __isl_keep isl_set *set1,
2175 __isl_keep isl_set *set2);
2176 int isl_union_set_is_subset(
2177 __isl_keep isl_union_set *uset1,
2178 __isl_keep isl_union_set *uset2);
2179 int isl_union_set_is_strict_subset(
2180 __isl_keep isl_union_set *uset1,
2181 __isl_keep isl_union_set *uset2);
2182 int isl_basic_map_is_subset(
2183 __isl_keep isl_basic_map *bmap1,
2184 __isl_keep isl_basic_map *bmap2);
2185 int isl_basic_map_is_strict_subset(
2186 __isl_keep isl_basic_map *bmap1,
2187 __isl_keep isl_basic_map *bmap2);
2188 int isl_map_is_subset(
2189 __isl_keep isl_map *map1,
2190 __isl_keep isl_map *map2);
2191 int isl_map_is_strict_subset(
2192 __isl_keep isl_map *map1,
2193 __isl_keep isl_map *map2);
2194 int isl_union_map_is_subset(
2195 __isl_keep isl_union_map *umap1,
2196 __isl_keep isl_union_map *umap2);
2197 int isl_union_map_is_strict_subset(
2198 __isl_keep isl_union_map *umap1,
2199 __isl_keep isl_union_map *umap2);
2201 Check whether the first argument is a (strict) subset of the
2206 Every comparison function returns a negative value if the first
2207 argument is considered smaller than the second, a positive value
2208 if the first argument is considered greater and zero if the two
2209 constraints are considered the same by the comparison criterion.
2211 #include <isl/constraint.h>
2212 int isl_constraint_plain_cmp(
2213 __isl_keep isl_constraint *c1,
2214 __isl_keep isl_constraint *c2);
2216 This function is useful for sorting C<isl_constraint>s.
2217 The order depends on the internal representation of the inputs.
2218 The order is fixed over different calls to the function (assuming
2219 the internal representation of the inputs has not changed), but may
2220 change over different versions of C<isl>.
2222 #include <isl/constraint.h>
2223 int isl_constraint_cmp_last_non_zero(
2224 __isl_keep isl_constraint *c1,
2225 __isl_keep isl_constraint *c2);
2227 This function can be used to sort constraints that live in the same
2228 local space. Constraints that involve ``earlier'' dimensions or
2229 that have a smaller coefficient for the shared latest dimension
2230 are considered smaller than other constraints.
2231 This function only defines a B<partial> order.
2233 #include <isl/set.h>
2234 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2235 __isl_keep isl_set *set2);
2237 This function is useful for sorting C<isl_set>s.
2238 The order depends on the internal representation of the inputs.
2239 The order is fixed over different calls to the function (assuming
2240 the internal representation of the inputs has not changed), but may
2241 change over different versions of C<isl>.
2245 =head2 Unary Operations
2251 __isl_give isl_set *isl_set_complement(
2252 __isl_take isl_set *set);
2253 __isl_give isl_map *isl_map_complement(
2254 __isl_take isl_map *map);
2258 __isl_give isl_basic_map *isl_basic_map_reverse(
2259 __isl_take isl_basic_map *bmap);
2260 __isl_give isl_map *isl_map_reverse(
2261 __isl_take isl_map *map);
2262 __isl_give isl_union_map *isl_union_map_reverse(
2263 __isl_take isl_union_map *umap);
2267 #include <isl/local_space.h>
2268 __isl_give isl_local_space *isl_local_space_domain(
2269 __isl_take isl_local_space *ls);
2270 __isl_give isl_local_space *isl_local_space_range(
2271 __isl_take isl_local_space *ls);
2273 #include <isl/set.h>
2274 __isl_give isl_basic_set *isl_basic_set_project_out(
2275 __isl_take isl_basic_set *bset,
2276 enum isl_dim_type type, unsigned first, unsigned n);
2277 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2278 enum isl_dim_type type, unsigned first, unsigned n);
2279 __isl_give isl_basic_set *isl_basic_set_params(
2280 __isl_take isl_basic_set *bset);
2281 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2283 #include <isl/map.h>
2284 __isl_give isl_basic_map *isl_basic_map_project_out(
2285 __isl_take isl_basic_map *bmap,
2286 enum isl_dim_type type, unsigned first, unsigned n);
2287 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2288 enum isl_dim_type type, unsigned first, unsigned n);
2289 __isl_give isl_basic_set *isl_basic_map_domain(
2290 __isl_take isl_basic_map *bmap);
2291 __isl_give isl_basic_set *isl_basic_map_range(
2292 __isl_take isl_basic_map *bmap);
2293 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2294 __isl_give isl_set *isl_map_domain(
2295 __isl_take isl_map *bmap);
2296 __isl_give isl_set *isl_map_range(
2297 __isl_take isl_map *map);
2299 #include <isl/union_set.h>
2300 __isl_give isl_set *isl_union_set_params(
2301 __isl_take isl_union_set *uset);
2303 #include <isl/union_map.h>
2304 __isl_give isl_union_map *isl_union_map_project_out(
2305 __isl_take isl_union_map *umap,
2306 enum isl_dim_type type, unsigned first, unsigned n);
2307 __isl_give isl_set *isl_union_map_params(
2308 __isl_take isl_union_map *umap);
2309 __isl_give isl_union_set *isl_union_map_domain(
2310 __isl_take isl_union_map *umap);
2311 __isl_give isl_union_set *isl_union_map_range(
2312 __isl_take isl_union_map *umap);
2314 The function C<isl_union_map_project_out> can only project out
2317 #include <isl/map.h>
2318 __isl_give isl_basic_map *isl_basic_map_domain_map(
2319 __isl_take isl_basic_map *bmap);
2320 __isl_give isl_basic_map *isl_basic_map_range_map(
2321 __isl_take isl_basic_map *bmap);
2322 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2323 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2325 #include <isl/union_map.h>
2326 __isl_give isl_union_map *isl_union_map_domain_map(
2327 __isl_take isl_union_map *umap);
2328 __isl_give isl_union_map *isl_union_map_range_map(
2329 __isl_take isl_union_map *umap);
2331 The functions above construct a (basic, regular or union) relation
2332 that maps (a wrapped version of) the input relation to its domain or range.
2336 __isl_give isl_basic_set *isl_basic_set_eliminate(
2337 __isl_take isl_basic_set *bset,
2338 enum isl_dim_type type,
2339 unsigned first, unsigned n);
2340 __isl_give isl_set *isl_set_eliminate(
2341 __isl_take isl_set *set, enum isl_dim_type type,
2342 unsigned first, unsigned n);
2343 __isl_give isl_basic_map *isl_basic_map_eliminate(
2344 __isl_take isl_basic_map *bmap,
2345 enum isl_dim_type type,
2346 unsigned first, unsigned n);
2347 __isl_give isl_map *isl_map_eliminate(
2348 __isl_take isl_map *map, enum isl_dim_type type,
2349 unsigned first, unsigned n);
2351 Eliminate the coefficients for the given dimensions from the constraints,
2352 without removing the dimensions.
2354 =item * Constructing a relation from a set
2356 #include <isl/local_space.h>
2357 __isl_give isl_local_space *isl_local_space_from_domain(
2358 __isl_take isl_local_space *ls);
2360 #include <isl/map.h>
2361 __isl_give isl_map *isl_map_from_domain(
2362 __isl_take isl_set *set);
2363 __isl_give isl_map *isl_map_from_range(
2364 __isl_take isl_set *set);
2366 Create a relation with the given set as domain or range.
2367 The range or domain of the created relation is a zero-dimensional
2368 flat anonymous space.
2372 __isl_give isl_basic_set *isl_basic_set_fix_si(
2373 __isl_take isl_basic_set *bset,
2374 enum isl_dim_type type, unsigned pos, int value);
2375 __isl_give isl_basic_set *isl_basic_set_fix_val(
2376 __isl_take isl_basic_set *bset,
2377 enum isl_dim_type type, unsigned pos,
2378 __isl_take isl_val *v);
2379 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2380 enum isl_dim_type type, unsigned pos, int value);
2381 __isl_give isl_set *isl_set_fix_val(
2382 __isl_take isl_set *set,
2383 enum isl_dim_type type, unsigned pos,
2384 __isl_take isl_val *v);
2385 __isl_give isl_basic_map *isl_basic_map_fix_si(
2386 __isl_take isl_basic_map *bmap,
2387 enum isl_dim_type type, unsigned pos, int value);
2388 __isl_give isl_basic_map *isl_basic_map_fix_val(
2389 __isl_take isl_basic_map *bmap,
2390 enum isl_dim_type type, unsigned pos,
2391 __isl_take isl_val *v);
2392 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2393 enum isl_dim_type type, unsigned pos, int value);
2394 __isl_give isl_map *isl_map_fix_val(
2395 __isl_take isl_map *map,
2396 enum isl_dim_type type, unsigned pos,
2397 __isl_take isl_val *v);
2399 Intersect the set or relation with the hyperplane where the given
2400 dimension has the fixed given value.
2402 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2403 __isl_take isl_basic_map *bmap,
2404 enum isl_dim_type type, unsigned pos, int value);
2405 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2406 __isl_take isl_basic_map *bmap,
2407 enum isl_dim_type type, unsigned pos, int value);
2408 __isl_give isl_set *isl_set_lower_bound_si(
2409 __isl_take isl_set *set,
2410 enum isl_dim_type type, unsigned pos, int value);
2411 __isl_give isl_set *isl_set_lower_bound_val(
2412 __isl_take isl_set *set,
2413 enum isl_dim_type type, unsigned pos,
2414 __isl_take isl_val *value);
2415 __isl_give isl_map *isl_map_lower_bound_si(
2416 __isl_take isl_map *map,
2417 enum isl_dim_type type, unsigned pos, int value);
2418 __isl_give isl_set *isl_set_upper_bound_si(
2419 __isl_take isl_set *set,
2420 enum isl_dim_type type, unsigned pos, int value);
2421 __isl_give isl_set *isl_set_upper_bound_val(
2422 __isl_take isl_set *set,
2423 enum isl_dim_type type, unsigned pos,
2424 __isl_take isl_val *value);
2425 __isl_give isl_map *isl_map_upper_bound_si(
2426 __isl_take isl_map *map,
2427 enum isl_dim_type type, unsigned pos, int value);
2429 Intersect the set or relation with the half-space where the given
2430 dimension has a value bounded by the fixed given integer value.
2432 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2433 enum isl_dim_type type1, int pos1,
2434 enum isl_dim_type type2, int pos2);
2435 __isl_give isl_basic_map *isl_basic_map_equate(
2436 __isl_take isl_basic_map *bmap,
2437 enum isl_dim_type type1, int pos1,
2438 enum isl_dim_type type2, int pos2);
2439 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2440 enum isl_dim_type type1, int pos1,
2441 enum isl_dim_type type2, int pos2);
2443 Intersect the set or relation with the hyperplane where the given
2444 dimensions are equal to each other.
2446 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2447 enum isl_dim_type type1, int pos1,
2448 enum isl_dim_type type2, int pos2);
2450 Intersect the relation with the hyperplane where the given
2451 dimensions have opposite values.
2453 __isl_give isl_map *isl_map_order_le(
2454 __isl_take isl_map *map,
2455 enum isl_dim_type type1, int pos1,
2456 enum isl_dim_type type2, int pos2);
2457 __isl_give isl_basic_map *isl_basic_map_order_ge(
2458 __isl_take isl_basic_map *bmap,
2459 enum isl_dim_type type1, int pos1,
2460 enum isl_dim_type type2, int pos2);
2461 __isl_give isl_map *isl_map_order_ge(
2462 __isl_take isl_map *map,
2463 enum isl_dim_type type1, int pos1,
2464 enum isl_dim_type type2, int pos2);
2465 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2466 enum isl_dim_type type1, int pos1,
2467 enum isl_dim_type type2, int pos2);
2468 __isl_give isl_basic_map *isl_basic_map_order_gt(
2469 __isl_take isl_basic_map *bmap,
2470 enum isl_dim_type type1, int pos1,
2471 enum isl_dim_type type2, int pos2);
2472 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2473 enum isl_dim_type type1, int pos1,
2474 enum isl_dim_type type2, int pos2);
2476 Intersect the relation with the half-space where the given
2477 dimensions satisfy the given ordering.
2481 __isl_give isl_map *isl_set_identity(
2482 __isl_take isl_set *set);
2483 __isl_give isl_union_map *isl_union_set_identity(
2484 __isl_take isl_union_set *uset);
2486 Construct an identity relation on the given (union) set.
2490 __isl_give isl_basic_set *isl_basic_map_deltas(
2491 __isl_take isl_basic_map *bmap);
2492 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2493 __isl_give isl_union_set *isl_union_map_deltas(
2494 __isl_take isl_union_map *umap);
2496 These functions return a (basic) set containing the differences
2497 between image elements and corresponding domain elements in the input.
2499 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2500 __isl_take isl_basic_map *bmap);
2501 __isl_give isl_map *isl_map_deltas_map(
2502 __isl_take isl_map *map);
2503 __isl_give isl_union_map *isl_union_map_deltas_map(
2504 __isl_take isl_union_map *umap);
2506 The functions above construct a (basic, regular or union) relation
2507 that maps (a wrapped version of) the input relation to its delta set.
2511 Simplify the representation of a set or relation by trying
2512 to combine pairs of basic sets or relations into a single
2513 basic set or relation.
2515 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2516 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2517 __isl_give isl_union_set *isl_union_set_coalesce(
2518 __isl_take isl_union_set *uset);
2519 __isl_give isl_union_map *isl_union_map_coalesce(
2520 __isl_take isl_union_map *umap);
2522 One of the methods for combining pairs of basic sets or relations
2523 can result in coefficients that are much larger than those that appear
2524 in the constraints of the input. By default, the coefficients are
2525 not allowed to grow larger, but this can be changed by unsetting
2526 the following option.
2528 int isl_options_set_coalesce_bounded_wrapping(
2529 isl_ctx *ctx, int val);
2530 int isl_options_get_coalesce_bounded_wrapping(
2533 =item * Detecting equalities
2535 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2536 __isl_take isl_basic_set *bset);
2537 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2538 __isl_take isl_basic_map *bmap);
2539 __isl_give isl_set *isl_set_detect_equalities(
2540 __isl_take isl_set *set);
2541 __isl_give isl_map *isl_map_detect_equalities(
2542 __isl_take isl_map *map);
2543 __isl_give isl_union_set *isl_union_set_detect_equalities(
2544 __isl_take isl_union_set *uset);
2545 __isl_give isl_union_map *isl_union_map_detect_equalities(
2546 __isl_take isl_union_map *umap);
2548 Simplify the representation of a set or relation by detecting implicit
2551 =item * Removing redundant constraints
2553 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2554 __isl_take isl_basic_set *bset);
2555 __isl_give isl_set *isl_set_remove_redundancies(
2556 __isl_take isl_set *set);
2557 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2558 __isl_take isl_basic_map *bmap);
2559 __isl_give isl_map *isl_map_remove_redundancies(
2560 __isl_take isl_map *map);
2564 __isl_give isl_basic_set *isl_set_convex_hull(
2565 __isl_take isl_set *set);
2566 __isl_give isl_basic_map *isl_map_convex_hull(
2567 __isl_take isl_map *map);
2569 If the input set or relation has any existentially quantified
2570 variables, then the result of these operations is currently undefined.
2574 __isl_give isl_basic_set *
2575 isl_set_unshifted_simple_hull(
2576 __isl_take isl_set *set);
2577 __isl_give isl_basic_map *
2578 isl_map_unshifted_simple_hull(
2579 __isl_take isl_map *map);
2580 __isl_give isl_basic_set *isl_set_simple_hull(
2581 __isl_take isl_set *set);
2582 __isl_give isl_basic_map *isl_map_simple_hull(
2583 __isl_take isl_map *map);
2584 __isl_give isl_union_map *isl_union_map_simple_hull(
2585 __isl_take isl_union_map *umap);
2587 These functions compute a single basic set or relation
2588 that contains the whole input set or relation.
2589 In particular, the output is described by translates
2590 of the constraints describing the basic sets or relations in the input.
2591 In case of C<isl_set_unshifted_simple_hull>, only the original
2592 constraints are used, without any translation.
2596 (See \autoref{s:simple hull}.)
2602 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2603 __isl_take isl_basic_set *bset);
2604 __isl_give isl_basic_set *isl_set_affine_hull(
2605 __isl_take isl_set *set);
2606 __isl_give isl_union_set *isl_union_set_affine_hull(
2607 __isl_take isl_union_set *uset);
2608 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2609 __isl_take isl_basic_map *bmap);
2610 __isl_give isl_basic_map *isl_map_affine_hull(
2611 __isl_take isl_map *map);
2612 __isl_give isl_union_map *isl_union_map_affine_hull(
2613 __isl_take isl_union_map *umap);
2615 In case of union sets and relations, the affine hull is computed
2618 =item * Polyhedral hull
2620 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2621 __isl_take isl_set *set);
2622 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2623 __isl_take isl_map *map);
2624 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2625 __isl_take isl_union_set *uset);
2626 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2627 __isl_take isl_union_map *umap);
2629 These functions compute a single basic set or relation
2630 not involving any existentially quantified variables
2631 that contains the whole input set or relation.
2632 In case of union sets and relations, the polyhedral hull is computed
2635 =item * Other approximations
2637 __isl_give isl_basic_set *
2638 isl_basic_set_drop_constraints_involving_dims(
2639 __isl_take isl_basic_set *bset,
2640 enum isl_dim_type type,
2641 unsigned first, unsigned n);
2642 __isl_give isl_basic_map *
2643 isl_basic_map_drop_constraints_involving_dims(
2644 __isl_take isl_basic_map *bmap,
2645 enum isl_dim_type type,
2646 unsigned first, unsigned n);
2647 __isl_give isl_basic_set *
2648 isl_basic_set_drop_constraints_not_involving_dims(
2649 __isl_take isl_basic_set *bset,
2650 enum isl_dim_type type,
2651 unsigned first, unsigned n);
2652 __isl_give isl_set *
2653 isl_set_drop_constraints_involving_dims(
2654 __isl_take isl_set *set,
2655 enum isl_dim_type type,
2656 unsigned first, unsigned n);
2657 __isl_give isl_map *
2658 isl_map_drop_constraints_involving_dims(
2659 __isl_take isl_map *map,
2660 enum isl_dim_type type,
2661 unsigned first, unsigned n);
2663 These functions drop any constraints (not) involving the specified dimensions.
2664 Note that the result depends on the representation of the input.
2668 __isl_give isl_basic_set *isl_basic_set_sample(
2669 __isl_take isl_basic_set *bset);
2670 __isl_give isl_basic_set *isl_set_sample(
2671 __isl_take isl_set *set);
2672 __isl_give isl_basic_map *isl_basic_map_sample(
2673 __isl_take isl_basic_map *bmap);
2674 __isl_give isl_basic_map *isl_map_sample(
2675 __isl_take isl_map *map);
2677 If the input (basic) set or relation is non-empty, then return
2678 a singleton subset of the input. Otherwise, return an empty set.
2680 =item * Optimization
2682 #include <isl/ilp.h>
2683 __isl_give isl_val *isl_basic_set_max_val(
2684 __isl_keep isl_basic_set *bset,
2685 __isl_keep isl_aff *obj);
2686 __isl_give isl_val *isl_set_min_val(
2687 __isl_keep isl_set *set,
2688 __isl_keep isl_aff *obj);
2689 __isl_give isl_val *isl_set_max_val(
2690 __isl_keep isl_set *set,
2691 __isl_keep isl_aff *obj);
2693 Compute the minimum or maximum of the integer affine expression C<obj>
2694 over the points in C<set>, returning the result in C<opt>.
2695 The result is C<NULL> in case of an error, the optimal value in case
2696 there is one, negative infinity or infinity if the problem is unbounded and
2697 NaN if the problem is empty.
2699 =item * Parametric optimization
2701 __isl_give isl_pw_aff *isl_set_dim_min(
2702 __isl_take isl_set *set, int pos);
2703 __isl_give isl_pw_aff *isl_set_dim_max(
2704 __isl_take isl_set *set, int pos);
2705 __isl_give isl_pw_aff *isl_map_dim_max(
2706 __isl_take isl_map *map, int pos);
2708 Compute the minimum or maximum of the given set or output dimension
2709 as a function of the parameters (and input dimensions), but independently
2710 of the other set or output dimensions.
2711 For lexicographic optimization, see L<"Lexicographic Optimization">.
2715 The following functions compute either the set of (rational) coefficient
2716 values of valid constraints for the given set or the set of (rational)
2717 values satisfying the constraints with coefficients from the given set.
2718 Internally, these two sets of functions perform essentially the
2719 same operations, except that the set of coefficients is assumed to
2720 be a cone, while the set of values may be any polyhedron.
2721 The current implementation is based on the Farkas lemma and
2722 Fourier-Motzkin elimination, but this may change or be made optional
2723 in future. In particular, future implementations may use different
2724 dualization algorithms or skip the elimination step.
2726 __isl_give isl_basic_set *isl_basic_set_coefficients(
2727 __isl_take isl_basic_set *bset);
2728 __isl_give isl_basic_set *isl_set_coefficients(
2729 __isl_take isl_set *set);
2730 __isl_give isl_union_set *isl_union_set_coefficients(
2731 __isl_take isl_union_set *bset);
2732 __isl_give isl_basic_set *isl_basic_set_solutions(
2733 __isl_take isl_basic_set *bset);
2734 __isl_give isl_basic_set *isl_set_solutions(
2735 __isl_take isl_set *set);
2736 __isl_give isl_union_set *isl_union_set_solutions(
2737 __isl_take isl_union_set *bset);
2741 __isl_give isl_map *isl_map_fixed_power_val(
2742 __isl_take isl_map *map,
2743 __isl_take isl_val *exp);
2744 __isl_give isl_union_map *
2745 isl_union_map_fixed_power_val(
2746 __isl_take isl_union_map *umap,
2747 __isl_take isl_val *exp);
2749 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2750 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2751 of C<map> is computed.
2753 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2755 __isl_give isl_union_map *isl_union_map_power(
2756 __isl_take isl_union_map *umap, int *exact);
2758 Compute a parametric representation for all positive powers I<k> of C<map>.
2759 The result maps I<k> to a nested relation corresponding to the
2760 I<k>th power of C<map>.
2761 The result may be an overapproximation. If the result is known to be exact,
2762 then C<*exact> is set to C<1>.
2764 =item * Transitive closure
2766 __isl_give isl_map *isl_map_transitive_closure(
2767 __isl_take isl_map *map, int *exact);
2768 __isl_give isl_union_map *isl_union_map_transitive_closure(
2769 __isl_take isl_union_map *umap, int *exact);
2771 Compute the transitive closure of C<map>.
2772 The result may be an overapproximation. If the result is known to be exact,
2773 then C<*exact> is set to C<1>.
2775 =item * Reaching path lengths
2777 __isl_give isl_map *isl_map_reaching_path_lengths(
2778 __isl_take isl_map *map, int *exact);
2780 Compute a relation that maps each element in the range of C<map>
2781 to the lengths of all paths composed of edges in C<map> that
2782 end up in the given element.
2783 The result may be an overapproximation. If the result is known to be exact,
2784 then C<*exact> is set to C<1>.
2785 To compute the I<maximal> path length, the resulting relation
2786 should be postprocessed by C<isl_map_lexmax>.
2787 In particular, if the input relation is a dependence relation
2788 (mapping sources to sinks), then the maximal path length corresponds
2789 to the free schedule.
2790 Note, however, that C<isl_map_lexmax> expects the maximum to be
2791 finite, so if the path lengths are unbounded (possibly due to
2792 the overapproximation), then you will get an error message.
2796 #include <isl/space.h>
2797 __isl_give isl_space *isl_space_wrap(
2798 __isl_take isl_space *space);
2799 __isl_give isl_space *isl_space_unwrap(
2800 __isl_take isl_space *space);
2802 #include <isl/set.h>
2803 __isl_give isl_basic_map *isl_basic_set_unwrap(
2804 __isl_take isl_basic_set *bset);
2805 __isl_give isl_map *isl_set_unwrap(
2806 __isl_take isl_set *set);
2808 #include <isl/map.h>
2809 __isl_give isl_basic_set *isl_basic_map_wrap(
2810 __isl_take isl_basic_map *bmap);
2811 __isl_give isl_set *isl_map_wrap(
2812 __isl_take isl_map *map);
2814 #include <isl/union_set.h>
2815 __isl_give isl_union_map *isl_union_set_unwrap(
2816 __isl_take isl_union_set *uset);
2818 #include <isl/union_map.h>
2819 __isl_give isl_union_set *isl_union_map_wrap(
2820 __isl_take isl_union_map *umap);
2822 The input to C<isl_space_unwrap> should
2823 be the space of a set, while that of
2824 C<isl_space_wrap> should be the space of a relation.
2825 Conversely, the output of C<isl_space_unwrap> is the space
2826 of a relation, while that of C<isl_space_wrap> is the space of a set.
2830 Remove any internal structure of domain (and range) of the given
2831 set or relation. If there is any such internal structure in the input,
2832 then the name of the space is also removed.
2834 #include <isl/local_space.h>
2835 __isl_give isl_local_space *
2836 isl_local_space_flatten_domain(
2837 __isl_take isl_local_space *ls);
2838 __isl_give isl_local_space *
2839 isl_local_space_flatten_range(
2840 __isl_take isl_local_space *ls);
2842 #include <isl/set.h>
2843 __isl_give isl_basic_set *isl_basic_set_flatten(
2844 __isl_take isl_basic_set *bset);
2845 __isl_give isl_set *isl_set_flatten(
2846 __isl_take isl_set *set);
2848 #include <isl/map.h>
2849 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2850 __isl_take isl_basic_map *bmap);
2851 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2852 __isl_take isl_basic_map *bmap);
2853 __isl_give isl_map *isl_map_flatten_range(
2854 __isl_take isl_map *map);
2855 __isl_give isl_map *isl_map_flatten_domain(
2856 __isl_take isl_map *map);
2857 __isl_give isl_basic_map *isl_basic_map_flatten(
2858 __isl_take isl_basic_map *bmap);
2859 __isl_give isl_map *isl_map_flatten(
2860 __isl_take isl_map *map);
2862 #include <isl/map.h>
2863 __isl_give isl_map *isl_set_flatten_map(
2864 __isl_take isl_set *set);
2866 The function above constructs a relation
2867 that maps the input set to a flattened version of the set.
2871 Lift the input set to a space with extra dimensions corresponding
2872 to the existentially quantified variables in the input.
2873 In particular, the result lives in a wrapped map where the domain
2874 is the original space and the range corresponds to the original
2875 existentially quantified variables.
2877 __isl_give isl_basic_set *isl_basic_set_lift(
2878 __isl_take isl_basic_set *bset);
2879 __isl_give isl_set *isl_set_lift(
2880 __isl_take isl_set *set);
2881 __isl_give isl_union_set *isl_union_set_lift(
2882 __isl_take isl_union_set *uset);
2884 Given a local space that contains the existentially quantified
2885 variables of a set, a basic relation that, when applied to
2886 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2887 can be constructed using the following function.
2889 #include <isl/local_space.h>
2890 __isl_give isl_basic_map *isl_local_space_lifting(
2891 __isl_take isl_local_space *ls);
2893 =item * Internal Product
2895 __isl_give isl_basic_map *isl_basic_map_zip(
2896 __isl_take isl_basic_map *bmap);
2897 __isl_give isl_map *isl_map_zip(
2898 __isl_take isl_map *map);
2899 __isl_give isl_union_map *isl_union_map_zip(
2900 __isl_take isl_union_map *umap);
2902 Given a relation with nested relations for domain and range,
2903 interchange the range of the domain with the domain of the range.
2907 __isl_give isl_basic_map *isl_basic_map_curry(
2908 __isl_take isl_basic_map *bmap);
2909 __isl_give isl_basic_map *isl_basic_map_uncurry(
2910 __isl_take isl_basic_map *bmap);
2911 __isl_give isl_map *isl_map_curry(
2912 __isl_take isl_map *map);
2913 __isl_give isl_map *isl_map_uncurry(
2914 __isl_take isl_map *map);
2915 __isl_give isl_union_map *isl_union_map_curry(
2916 __isl_take isl_union_map *umap);
2917 __isl_give isl_union_map *isl_union_map_uncurry(
2918 __isl_take isl_union_map *umap);
2920 Given a relation with a nested relation for domain,
2921 the C<curry> functions
2922 move the range of the nested relation out of the domain
2923 and use it as the domain of a nested relation in the range,
2924 with the original range as range of this nested relation.
2925 The C<uncurry> functions perform the inverse operation.
2927 =item * Aligning parameters
2929 __isl_give isl_basic_set *isl_basic_set_align_params(
2930 __isl_take isl_basic_set *bset,
2931 __isl_take isl_space *model);
2932 __isl_give isl_set *isl_set_align_params(
2933 __isl_take isl_set *set,
2934 __isl_take isl_space *model);
2935 __isl_give isl_basic_map *isl_basic_map_align_params(
2936 __isl_take isl_basic_map *bmap,
2937 __isl_take isl_space *model);
2938 __isl_give isl_map *isl_map_align_params(
2939 __isl_take isl_map *map,
2940 __isl_take isl_space *model);
2942 Change the order of the parameters of the given set or relation
2943 such that the first parameters match those of C<model>.
2944 This may involve the introduction of extra parameters.
2945 All parameters need to be named.
2947 =item * Dimension manipulation
2949 #include <isl/local_space.h>
2950 __isl_give isl_local_space *isl_local_space_add_dims(
2951 __isl_take isl_local_space *ls,
2952 enum isl_dim_type type, unsigned n);
2953 __isl_give isl_local_space *isl_local_space_insert_dims(
2954 __isl_take isl_local_space *ls,
2955 enum isl_dim_type type, unsigned first, unsigned n);
2956 __isl_give isl_local_space *isl_local_space_drop_dims(
2957 __isl_take isl_local_space *ls,
2958 enum isl_dim_type type, unsigned first, unsigned n);
2960 #include <isl/set.h>
2961 __isl_give isl_basic_set *isl_basic_set_add_dims(
2962 __isl_take isl_basic_set *bset,
2963 enum isl_dim_type type, unsigned n);
2964 __isl_give isl_set *isl_set_add_dims(
2965 __isl_take isl_set *set,
2966 enum isl_dim_type type, unsigned n);
2967 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2968 __isl_take isl_basic_set *bset,
2969 enum isl_dim_type type, unsigned pos,
2971 __isl_give isl_set *isl_set_insert_dims(
2972 __isl_take isl_set *set,
2973 enum isl_dim_type type, unsigned pos, unsigned n);
2974 __isl_give isl_basic_set *isl_basic_set_move_dims(
2975 __isl_take isl_basic_set *bset,
2976 enum isl_dim_type dst_type, unsigned dst_pos,
2977 enum isl_dim_type src_type, unsigned src_pos,
2979 __isl_give isl_set *isl_set_move_dims(
2980 __isl_take isl_set *set,
2981 enum isl_dim_type dst_type, unsigned dst_pos,
2982 enum isl_dim_type src_type, unsigned src_pos,
2985 #include <isl/map.h>
2986 __isl_give isl_map *isl_map_add_dims(
2987 __isl_take isl_map *map,
2988 enum isl_dim_type type, unsigned n);
2989 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2990 __isl_take isl_basic_map *bmap,
2991 enum isl_dim_type type, unsigned pos,
2993 __isl_give isl_map *isl_map_insert_dims(
2994 __isl_take isl_map *map,
2995 enum isl_dim_type type, unsigned pos, unsigned n);
2996 __isl_give isl_basic_map *isl_basic_map_move_dims(
2997 __isl_take isl_basic_map *bmap,
2998 enum isl_dim_type dst_type, unsigned dst_pos,
2999 enum isl_dim_type src_type, unsigned src_pos,
3001 __isl_give isl_map *isl_map_move_dims(
3002 __isl_take isl_map *map,
3003 enum isl_dim_type dst_type, unsigned dst_pos,
3004 enum isl_dim_type src_type, unsigned src_pos,
3007 It is usually not advisable to directly change the (input or output)
3008 space of a set or a relation as this removes the name and the internal
3009 structure of the space. However, the above functions can be useful
3010 to add new parameters, assuming
3011 C<isl_set_align_params> and C<isl_map_align_params>
3016 =head2 Binary Operations
3018 The two arguments of a binary operation not only need to live
3019 in the same C<isl_ctx>, they currently also need to have
3020 the same (number of) parameters.
3022 =head3 Basic Operations
3026 =item * Intersection
3028 #include <isl/local_space.h>
3029 __isl_give isl_local_space *isl_local_space_intersect(
3030 __isl_take isl_local_space *ls1,
3031 __isl_take isl_local_space *ls2);
3033 #include <isl/set.h>
3034 __isl_give isl_basic_set *isl_basic_set_intersect_params(
3035 __isl_take isl_basic_set *bset1,
3036 __isl_take isl_basic_set *bset2);
3037 __isl_give isl_basic_set *isl_basic_set_intersect(
3038 __isl_take isl_basic_set *bset1,
3039 __isl_take isl_basic_set *bset2);
3040 __isl_give isl_basic_set *isl_basic_set_list_intersect(
3041 __isl_take struct isl_basic_set_list *list);
3042 __isl_give isl_set *isl_set_intersect_params(
3043 __isl_take isl_set *set,
3044 __isl_take isl_set *params);
3045 __isl_give isl_set *isl_set_intersect(
3046 __isl_take isl_set *set1,
3047 __isl_take isl_set *set2);
3049 #include <isl/map.h>
3050 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
3051 __isl_take isl_basic_map *bmap,
3052 __isl_take isl_basic_set *bset);
3053 __isl_give isl_basic_map *isl_basic_map_intersect_range(
3054 __isl_take isl_basic_map *bmap,
3055 __isl_take isl_basic_set *bset);
3056 __isl_give isl_basic_map *isl_basic_map_intersect(
3057 __isl_take isl_basic_map *bmap1,
3058 __isl_take isl_basic_map *bmap2);
3059 __isl_give isl_map *isl_map_intersect_params(
3060 __isl_take isl_map *map,
3061 __isl_take isl_set *params);
3062 __isl_give isl_map *isl_map_intersect_domain(
3063 __isl_take isl_map *map,
3064 __isl_take isl_set *set);
3065 __isl_give isl_map *isl_map_intersect_range(
3066 __isl_take isl_map *map,
3067 __isl_take isl_set *set);
3068 __isl_give isl_map *isl_map_intersect(
3069 __isl_take isl_map *map1,
3070 __isl_take isl_map *map2);
3072 #include <isl/union_set.h>
3073 __isl_give isl_union_set *isl_union_set_intersect_params(
3074 __isl_take isl_union_set *uset,
3075 __isl_take isl_set *set);
3076 __isl_give isl_union_set *isl_union_set_intersect(
3077 __isl_take isl_union_set *uset1,
3078 __isl_take isl_union_set *uset2);
3080 #include <isl/union_map.h>
3081 __isl_give isl_union_map *isl_union_map_intersect_params(
3082 __isl_take isl_union_map *umap,
3083 __isl_take isl_set *set);
3084 __isl_give isl_union_map *isl_union_map_intersect_domain(
3085 __isl_take isl_union_map *umap,
3086 __isl_take isl_union_set *uset);
3087 __isl_give isl_union_map *isl_union_map_intersect_range(
3088 __isl_take isl_union_map *umap,
3089 __isl_take isl_union_set *uset);
3090 __isl_give isl_union_map *isl_union_map_intersect(
3091 __isl_take isl_union_map *umap1,
3092 __isl_take isl_union_map *umap2);
3094 The second argument to the C<_params> functions needs to be
3095 a parametric (basic) set. For the other functions, a parametric set
3096 for either argument is only allowed if the other argument is
3097 a parametric set as well.
3098 The list passed to C<isl_basic_set_list_intersect> needs to have
3099 at least one element and all elements need to live in the same space.
3103 __isl_give isl_set *isl_basic_set_union(
3104 __isl_take isl_basic_set *bset1,
3105 __isl_take isl_basic_set *bset2);
3106 __isl_give isl_map *isl_basic_map_union(
3107 __isl_take isl_basic_map *bmap1,
3108 __isl_take isl_basic_map *bmap2);
3109 __isl_give isl_set *isl_set_union(
3110 __isl_take isl_set *set1,
3111 __isl_take isl_set *set2);
3112 __isl_give isl_map *isl_map_union(
3113 __isl_take isl_map *map1,
3114 __isl_take isl_map *map2);
3115 __isl_give isl_union_set *isl_union_set_union(
3116 __isl_take isl_union_set *uset1,
3117 __isl_take isl_union_set *uset2);
3118 __isl_give isl_union_map *isl_union_map_union(
3119 __isl_take isl_union_map *umap1,
3120 __isl_take isl_union_map *umap2);
3122 =item * Set difference
3124 __isl_give isl_set *isl_set_subtract(
3125 __isl_take isl_set *set1,
3126 __isl_take isl_set *set2);
3127 __isl_give isl_map *isl_map_subtract(
3128 __isl_take isl_map *map1,
3129 __isl_take isl_map *map2);
3130 __isl_give isl_map *isl_map_subtract_domain(
3131 __isl_take isl_map *map,
3132 __isl_take isl_set *dom);
3133 __isl_give isl_map *isl_map_subtract_range(
3134 __isl_take isl_map *map,
3135 __isl_take isl_set *dom);
3136 __isl_give isl_union_set *isl_union_set_subtract(
3137 __isl_take isl_union_set *uset1,
3138 __isl_take isl_union_set *uset2);
3139 __isl_give isl_union_map *isl_union_map_subtract(
3140 __isl_take isl_union_map *umap1,
3141 __isl_take isl_union_map *umap2);
3142 __isl_give isl_union_map *isl_union_map_subtract_domain(
3143 __isl_take isl_union_map *umap,
3144 __isl_take isl_union_set *dom);
3145 __isl_give isl_union_map *isl_union_map_subtract_range(
3146 __isl_take isl_union_map *umap,
3147 __isl_take isl_union_set *dom);
3151 __isl_give isl_basic_set *isl_basic_set_apply(
3152 __isl_take isl_basic_set *bset,
3153 __isl_take isl_basic_map *bmap);
3154 __isl_give isl_set *isl_set_apply(
3155 __isl_take isl_set *set,
3156 __isl_take isl_map *map);
3157 __isl_give isl_union_set *isl_union_set_apply(
3158 __isl_take isl_union_set *uset,
3159 __isl_take isl_union_map *umap);
3160 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3161 __isl_take isl_basic_map *bmap1,
3162 __isl_take isl_basic_map *bmap2);
3163 __isl_give isl_basic_map *isl_basic_map_apply_range(
3164 __isl_take isl_basic_map *bmap1,
3165 __isl_take isl_basic_map *bmap2);
3166 __isl_give isl_map *isl_map_apply_domain(
3167 __isl_take isl_map *map1,
3168 __isl_take isl_map *map2);
3169 __isl_give isl_union_map *isl_union_map_apply_domain(
3170 __isl_take isl_union_map *umap1,
3171 __isl_take isl_union_map *umap2);
3172 __isl_give isl_map *isl_map_apply_range(
3173 __isl_take isl_map *map1,
3174 __isl_take isl_map *map2);
3175 __isl_give isl_union_map *isl_union_map_apply_range(
3176 __isl_take isl_union_map *umap1,
3177 __isl_take isl_union_map *umap2);
3181 #include <isl/set.h>
3182 __isl_give isl_basic_set *
3183 isl_basic_set_preimage_multi_aff(
3184 __isl_take isl_basic_set *bset,
3185 __isl_take isl_multi_aff *ma);
3186 __isl_give isl_set *isl_set_preimage_multi_aff(
3187 __isl_take isl_set *set,
3188 __isl_take isl_multi_aff *ma);
3189 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3190 __isl_take isl_set *set,
3191 __isl_take isl_pw_multi_aff *pma);
3192 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3193 __isl_take isl_set *set,
3194 __isl_take isl_multi_pw_aff *mpa);
3196 #include <isl/union_set.h>
3197 __isl_give isl_union_set *
3198 isl_union_set_preimage_multi_aff(
3199 __isl_take isl_union_set *uset,
3200 __isl_take isl_multi_aff *ma);
3201 __isl_give isl_union_set *
3202 isl_union_set_preimage_pw_multi_aff(
3203 __isl_take isl_union_set *uset,
3204 __isl_take isl_pw_multi_aff *pma);
3205 __isl_give isl_union_set *
3206 isl_union_set_preimage_union_pw_multi_aff(
3207 __isl_take isl_union_set *uset,
3208 __isl_take isl_union_pw_multi_aff *upma);
3210 #include <isl/map.h>
3211 __isl_give isl_basic_map *
3212 isl_basic_map_preimage_domain_multi_aff(
3213 __isl_take isl_basic_map *bmap,
3214 __isl_take isl_multi_aff *ma);
3215 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3216 __isl_take isl_map *map,
3217 __isl_take isl_multi_aff *ma);
3218 __isl_give isl_map *isl_map_preimage_range_multi_aff(
3219 __isl_take isl_map *map,
3220 __isl_take isl_multi_aff *ma);
3221 __isl_give isl_map *
3222 isl_map_preimage_domain_pw_multi_aff(
3223 __isl_take isl_map *map,
3224 __isl_take isl_pw_multi_aff *pma);
3225 __isl_give isl_map *
3226 isl_map_preimage_range_pw_multi_aff(
3227 __isl_take isl_map *map,
3228 __isl_take isl_pw_multi_aff *pma);
3229 __isl_give isl_map *
3230 isl_map_preimage_domain_multi_pw_aff(
3231 __isl_take isl_map *map,
3232 __isl_take isl_multi_pw_aff *mpa);
3233 __isl_give isl_basic_map *
3234 isl_basic_map_preimage_range_multi_aff(
3235 __isl_take isl_basic_map *bmap,
3236 __isl_take isl_multi_aff *ma);
3238 #include <isl/union_map.h>
3239 __isl_give isl_union_map *
3240 isl_union_map_preimage_domain_multi_aff(
3241 __isl_take isl_union_map *umap,
3242 __isl_take isl_multi_aff *ma);
3243 __isl_give isl_union_map *
3244 isl_union_map_preimage_range_multi_aff(
3245 __isl_take isl_union_map *umap,
3246 __isl_take isl_multi_aff *ma);
3247 __isl_give isl_union_map *
3248 isl_union_map_preimage_domain_pw_multi_aff(
3249 __isl_take isl_union_map *umap,
3250 __isl_take isl_pw_multi_aff *pma);
3251 __isl_give isl_union_map *
3252 isl_union_map_preimage_range_pw_multi_aff(
3253 __isl_take isl_union_map *umap,
3254 __isl_take isl_pw_multi_aff *pma);
3255 __isl_give isl_union_map *
3256 isl_union_map_preimage_domain_union_pw_multi_aff(
3257 __isl_take isl_union_map *umap,
3258 __isl_take isl_union_pw_multi_aff *upma);
3259 __isl_give isl_union_map *
3260 isl_union_map_preimage_range_union_pw_multi_aff(
3261 __isl_take isl_union_map *umap,
3262 __isl_take isl_union_pw_multi_aff *upma);
3264 These functions compute the preimage of the given set or map domain/range under
3265 the given function. In other words, the expression is plugged
3266 into the set description or into the domain/range of the map.
3267 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3268 L</"Piecewise Multiple Quasi Affine Expressions">.
3270 =item * Cartesian Product
3272 #include <isl/space.h>
3273 __isl_give isl_space *isl_space_product(
3274 __isl_take isl_space *space1,
3275 __isl_take isl_space *space2);
3276 __isl_give isl_space *isl_space_domain_product(
3277 __isl_take isl_space *space1,
3278 __isl_take isl_space *space2);
3279 __isl_give isl_space *isl_space_range_product(
3280 __isl_take isl_space *space1,
3281 __isl_take isl_space *space2);
3284 C<isl_space_product>, C<isl_space_domain_product>
3285 and C<isl_space_range_product> take pairs or relation spaces and
3286 produce a single relations space, where either the domain, the range
3287 or both domain and range are wrapped spaces of relations between
3288 the domains and/or ranges of the input spaces.
3289 If the product is only constructed over the domain or the range
3290 then the ranges or the domains of the inputs should be the same.
3291 The function C<isl_space_product> also accepts a pair of set spaces,
3292 in which case it returns a wrapped space of a relation between the
3295 #include <isl/set.h>
3296 __isl_give isl_set *isl_set_product(
3297 __isl_take isl_set *set1,
3298 __isl_take isl_set *set2);
3300 #include <isl/map.h>
3301 __isl_give isl_basic_map *isl_basic_map_domain_product(
3302 __isl_take isl_basic_map *bmap1,
3303 __isl_take isl_basic_map *bmap2);
3304 __isl_give isl_basic_map *isl_basic_map_range_product(
3305 __isl_take isl_basic_map *bmap1,
3306 __isl_take isl_basic_map *bmap2);
3307 __isl_give isl_basic_map *isl_basic_map_product(
3308 __isl_take isl_basic_map *bmap1,
3309 __isl_take isl_basic_map *bmap2);
3310 __isl_give isl_map *isl_map_domain_product(
3311 __isl_take isl_map *map1,
3312 __isl_take isl_map *map2);
3313 __isl_give isl_map *isl_map_range_product(
3314 __isl_take isl_map *map1,
3315 __isl_take isl_map *map2);
3316 __isl_give isl_map *isl_map_product(
3317 __isl_take isl_map *map1,
3318 __isl_take isl_map *map2);
3320 #include <isl/union_set.h>
3321 __isl_give isl_union_set *isl_union_set_product(
3322 __isl_take isl_union_set *uset1,
3323 __isl_take isl_union_set *uset2);
3325 #include <isl/union_map.h>
3326 __isl_give isl_union_map *isl_union_map_domain_product(
3327 __isl_take isl_union_map *umap1,
3328 __isl_take isl_union_map *umap2);
3329 __isl_give isl_union_map *isl_union_map_range_product(
3330 __isl_take isl_union_map *umap1,
3331 __isl_take isl_union_map *umap2);
3332 __isl_give isl_union_map *isl_union_map_product(
3333 __isl_take isl_union_map *umap1,
3334 __isl_take isl_union_map *umap2);
3336 The above functions compute the cross product of the given
3337 sets or relations. The domains and ranges of the results
3338 are wrapped maps between domains and ranges of the inputs.
3339 To obtain a ``flat'' product, use the following functions
3342 __isl_give isl_basic_set *isl_basic_set_flat_product(
3343 __isl_take isl_basic_set *bset1,
3344 __isl_take isl_basic_set *bset2);
3345 __isl_give isl_set *isl_set_flat_product(
3346 __isl_take isl_set *set1,
3347 __isl_take isl_set *set2);
3348 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3349 __isl_take isl_basic_map *bmap1,
3350 __isl_take isl_basic_map *bmap2);
3351 __isl_give isl_map *isl_map_flat_domain_product(
3352 __isl_take isl_map *map1,
3353 __isl_take isl_map *map2);
3354 __isl_give isl_map *isl_map_flat_range_product(
3355 __isl_take isl_map *map1,
3356 __isl_take isl_map *map2);
3357 __isl_give isl_union_map *isl_union_map_flat_range_product(
3358 __isl_take isl_union_map *umap1,
3359 __isl_take isl_union_map *umap2);
3360 __isl_give isl_basic_map *isl_basic_map_flat_product(
3361 __isl_take isl_basic_map *bmap1,
3362 __isl_take isl_basic_map *bmap2);
3363 __isl_give isl_map *isl_map_flat_product(
3364 __isl_take isl_map *map1,
3365 __isl_take isl_map *map2);
3367 #include <isl/space.h>
3368 __isl_give isl_space *isl_space_domain_factor_domain(
3369 __isl_take isl_space *space);
3370 __isl_give isl_space *isl_space_range_factor_domain(
3371 __isl_take isl_space *space);
3372 __isl_give isl_space *isl_space_range_factor_range(
3373 __isl_take isl_space *space);
3375 The functions C<isl_space_range_factor_domain> and
3376 C<isl_space_range_factor_range> extract the two arguments from
3377 the result of a call to C<isl_space_range_product>.
3379 The arguments of a call to C<isl_map_range_product> can be extracted
3380 from the result using the following two functions.
3382 #include <isl/map.h>
3383 __isl_give isl_map *isl_map_range_factor_domain(
3384 __isl_take isl_map *map);
3385 __isl_give isl_map *isl_map_range_factor_range(
3386 __isl_take isl_map *map);
3388 =item * Simplification
3390 __isl_give isl_basic_set *isl_basic_set_gist(
3391 __isl_take isl_basic_set *bset,
3392 __isl_take isl_basic_set *context);
3393 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3394 __isl_take isl_set *context);
3395 __isl_give isl_set *isl_set_gist_params(
3396 __isl_take isl_set *set,
3397 __isl_take isl_set *context);
3398 __isl_give isl_union_set *isl_union_set_gist(
3399 __isl_take isl_union_set *uset,
3400 __isl_take isl_union_set *context);
3401 __isl_give isl_union_set *isl_union_set_gist_params(
3402 __isl_take isl_union_set *uset,
3403 __isl_take isl_set *set);
3404 __isl_give isl_basic_map *isl_basic_map_gist(
3405 __isl_take isl_basic_map *bmap,
3406 __isl_take isl_basic_map *context);
3407 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3408 __isl_take isl_map *context);
3409 __isl_give isl_map *isl_map_gist_params(
3410 __isl_take isl_map *map,
3411 __isl_take isl_set *context);
3412 __isl_give isl_map *isl_map_gist_domain(
3413 __isl_take isl_map *map,
3414 __isl_take isl_set *context);
3415 __isl_give isl_map *isl_map_gist_range(
3416 __isl_take isl_map *map,
3417 __isl_take isl_set *context);
3418 __isl_give isl_union_map *isl_union_map_gist(
3419 __isl_take isl_union_map *umap,
3420 __isl_take isl_union_map *context);
3421 __isl_give isl_union_map *isl_union_map_gist_params(
3422 __isl_take isl_union_map *umap,
3423 __isl_take isl_set *set);
3424 __isl_give isl_union_map *isl_union_map_gist_domain(
3425 __isl_take isl_union_map *umap,
3426 __isl_take isl_union_set *uset);
3427 __isl_give isl_union_map *isl_union_map_gist_range(
3428 __isl_take isl_union_map *umap,
3429 __isl_take isl_union_set *uset);
3431 The gist operation returns a set or relation that has the
3432 same intersection with the context as the input set or relation.
3433 Any implicit equality in the intersection is made explicit in the result,
3434 while all inequalities that are redundant with respect to the intersection
3436 In case of union sets and relations, the gist operation is performed
3441 =head3 Lexicographic Optimization
3443 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3444 the following functions
3445 compute a set that contains the lexicographic minimum or maximum
3446 of the elements in C<set> (or C<bset>) for those values of the parameters
3447 that satisfy C<dom>.
3448 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3449 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3451 In other words, the union of the parameter values
3452 for which the result is non-empty and of C<*empty>
3455 __isl_give isl_set *isl_basic_set_partial_lexmin(
3456 __isl_take isl_basic_set *bset,
3457 __isl_take isl_basic_set *dom,
3458 __isl_give isl_set **empty);
3459 __isl_give isl_set *isl_basic_set_partial_lexmax(
3460 __isl_take isl_basic_set *bset,
3461 __isl_take isl_basic_set *dom,
3462 __isl_give isl_set **empty);
3463 __isl_give isl_set *isl_set_partial_lexmin(
3464 __isl_take isl_set *set, __isl_take isl_set *dom,
3465 __isl_give isl_set **empty);
3466 __isl_give isl_set *isl_set_partial_lexmax(
3467 __isl_take isl_set *set, __isl_take isl_set *dom,
3468 __isl_give isl_set **empty);
3470 Given a (basic) set C<set> (or C<bset>), the following functions simply
3471 return a set containing the lexicographic minimum or maximum
3472 of the elements in C<set> (or C<bset>).
3473 In case of union sets, the optimum is computed per space.
3475 __isl_give isl_set *isl_basic_set_lexmin(
3476 __isl_take isl_basic_set *bset);
3477 __isl_give isl_set *isl_basic_set_lexmax(
3478 __isl_take isl_basic_set *bset);
3479 __isl_give isl_set *isl_set_lexmin(
3480 __isl_take isl_set *set);
3481 __isl_give isl_set *isl_set_lexmax(
3482 __isl_take isl_set *set);
3483 __isl_give isl_union_set *isl_union_set_lexmin(
3484 __isl_take isl_union_set *uset);
3485 __isl_give isl_union_set *isl_union_set_lexmax(
3486 __isl_take isl_union_set *uset);
3488 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3489 the following functions
3490 compute a relation that maps each element of C<dom>
3491 to the single lexicographic minimum or maximum
3492 of the elements that are associated to that same
3493 element in C<map> (or C<bmap>).
3494 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3495 that contains the elements in C<dom> that do not map
3496 to any elements in C<map> (or C<bmap>).
3497 In other words, the union of the domain of the result and of C<*empty>
3500 __isl_give isl_map *isl_basic_map_partial_lexmax(
3501 __isl_take isl_basic_map *bmap,
3502 __isl_take isl_basic_set *dom,
3503 __isl_give isl_set **empty);
3504 __isl_give isl_map *isl_basic_map_partial_lexmin(
3505 __isl_take isl_basic_map *bmap,
3506 __isl_take isl_basic_set *dom,
3507 __isl_give isl_set **empty);
3508 __isl_give isl_map *isl_map_partial_lexmax(
3509 __isl_take isl_map *map, __isl_take isl_set *dom,
3510 __isl_give isl_set **empty);
3511 __isl_give isl_map *isl_map_partial_lexmin(
3512 __isl_take isl_map *map, __isl_take isl_set *dom,
3513 __isl_give isl_set **empty);
3515 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3516 return a map mapping each element in the domain of
3517 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3518 of all elements associated to that element.
3519 In case of union relations, the optimum is computed per space.
3521 __isl_give isl_map *isl_basic_map_lexmin(
3522 __isl_take isl_basic_map *bmap);
3523 __isl_give isl_map *isl_basic_map_lexmax(
3524 __isl_take isl_basic_map *bmap);
3525 __isl_give isl_map *isl_map_lexmin(
3526 __isl_take isl_map *map);
3527 __isl_give isl_map *isl_map_lexmax(
3528 __isl_take isl_map *map);
3529 __isl_give isl_union_map *isl_union_map_lexmin(
3530 __isl_take isl_union_map *umap);
3531 __isl_give isl_union_map *isl_union_map_lexmax(
3532 __isl_take isl_union_map *umap);
3534 The following functions return their result in the form of
3535 a piecewise multi-affine expression
3536 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3537 but are otherwise equivalent to the corresponding functions
3538 returning a basic set or relation.
3540 __isl_give isl_pw_multi_aff *
3541 isl_basic_map_lexmin_pw_multi_aff(
3542 __isl_take isl_basic_map *bmap);
3543 __isl_give isl_pw_multi_aff *
3544 isl_basic_set_partial_lexmin_pw_multi_aff(
3545 __isl_take isl_basic_set *bset,
3546 __isl_take isl_basic_set *dom,
3547 __isl_give isl_set **empty);
3548 __isl_give isl_pw_multi_aff *
3549 isl_basic_set_partial_lexmax_pw_multi_aff(
3550 __isl_take isl_basic_set *bset,
3551 __isl_take isl_basic_set *dom,
3552 __isl_give isl_set **empty);
3553 __isl_give isl_pw_multi_aff *
3554 isl_basic_map_partial_lexmin_pw_multi_aff(
3555 __isl_take isl_basic_map *bmap,
3556 __isl_take isl_basic_set *dom,
3557 __isl_give isl_set **empty);
3558 __isl_give isl_pw_multi_aff *
3559 isl_basic_map_partial_lexmax_pw_multi_aff(
3560 __isl_take isl_basic_map *bmap,
3561 __isl_take isl_basic_set *dom,
3562 __isl_give isl_set **empty);
3563 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3564 __isl_take isl_set *set);
3565 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3566 __isl_take isl_set *set);
3567 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3568 __isl_take isl_map *map);
3569 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3570 __isl_take isl_map *map);
3574 Lists are defined over several element types, including
3575 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3576 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3577 Here we take lists of C<isl_set>s as an example.
3578 Lists can be created, copied, modified and freed using the following functions.
3580 #include <isl/list.h>
3581 __isl_give isl_set_list *isl_set_list_from_set(
3582 __isl_take isl_set *el);
3583 __isl_give isl_set_list *isl_set_list_alloc(
3584 isl_ctx *ctx, int n);
3585 __isl_give isl_set_list *isl_set_list_copy(
3586 __isl_keep isl_set_list *list);
3587 __isl_give isl_set_list *isl_set_list_insert(
3588 __isl_take isl_set_list *list, unsigned pos,
3589 __isl_take isl_set *el);
3590 __isl_give isl_set_list *isl_set_list_add(
3591 __isl_take isl_set_list *list,
3592 __isl_take isl_set *el);
3593 __isl_give isl_set_list *isl_set_list_drop(
3594 __isl_take isl_set_list *list,
3595 unsigned first, unsigned n);
3596 __isl_give isl_set_list *isl_set_list_set_set(
3597 __isl_take isl_set_list *list, int index,
3598 __isl_take isl_set *set);
3599 __isl_give isl_set_list *isl_set_list_concat(
3600 __isl_take isl_set_list *list1,
3601 __isl_take isl_set_list *list2);
3602 __isl_give isl_set_list *isl_set_list_sort(
3603 __isl_take isl_set_list *list,
3604 int (*cmp)(__isl_keep isl_set *a,
3605 __isl_keep isl_set *b, void *user),
3607 __isl_null isl_set_list *isl_set_list_free(
3608 __isl_take isl_set_list *list);
3610 C<isl_set_list_alloc> creates an empty list with a capacity for
3611 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3614 Lists can be inspected using the following functions.
3616 #include <isl/list.h>
3617 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3618 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3619 __isl_give isl_set *isl_set_list_get_set(
3620 __isl_keep isl_set_list *list, int index);
3621 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3622 int (*fn)(__isl_take isl_set *el, void *user),
3624 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3625 int (*follows)(__isl_keep isl_set *a,
3626 __isl_keep isl_set *b, void *user),
3628 int (*fn)(__isl_take isl_set *el, void *user),
3631 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3632 strongly connected components of the graph with as vertices the elements
3633 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3634 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3635 should return C<-1> on error.
3637 Lists can be printed using
3639 #include <isl/list.h>
3640 __isl_give isl_printer *isl_printer_print_set_list(
3641 __isl_take isl_printer *p,
3642 __isl_keep isl_set_list *list);
3644 =head2 Associative arrays
3646 Associative arrays map isl objects of a specific type to isl objects
3647 of some (other) specific type. They are defined for several pairs
3648 of types, including (C<isl_map>, C<isl_basic_set>),
3649 (C<isl_id>, C<isl_ast_expr>) and.
3650 (C<isl_id>, C<isl_pw_aff>).
3651 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3654 Associative arrays can be created, copied and freed using
3655 the following functions.
3657 #include <isl/id_to_ast_expr.h>
3658 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3659 isl_ctx *ctx, int min_size);
3660 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3661 __isl_keep id_to_ast_expr *id2expr);
3662 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
3663 __isl_take id_to_ast_expr *id2expr);
3665 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3666 to specify the expected size of the associative array.
3667 The associative array will be grown automatically as needed.
3669 Associative arrays can be inspected using the following functions.
3671 #include <isl/id_to_ast_expr.h>
3672 isl_ctx *isl_id_to_ast_expr_get_ctx(
3673 __isl_keep id_to_ast_expr *id2expr);
3674 int isl_id_to_ast_expr_has(
3675 __isl_keep id_to_ast_expr *id2expr,
3676 __isl_keep isl_id *key);
3677 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3678 __isl_keep id_to_ast_expr *id2expr,
3679 __isl_take isl_id *key);
3680 int isl_id_to_ast_expr_foreach(
3681 __isl_keep id_to_ast_expr *id2expr,
3682 int (*fn)(__isl_take isl_id *key,
3683 __isl_take isl_ast_expr *val, void *user),
3686 They can be modified using the following function.
3688 #include <isl/id_to_ast_expr.h>
3689 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3690 __isl_take id_to_ast_expr *id2expr,
3691 __isl_take isl_id *key,
3692 __isl_take isl_ast_expr *val);
3693 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3694 __isl_take id_to_ast_expr *id2expr,
3695 __isl_take isl_id *key);
3697 Associative arrays can be printed using the following function.
3699 #include <isl/id_to_ast_expr.h>
3700 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3701 __isl_take isl_printer *p,
3702 __isl_keep id_to_ast_expr *id2expr);
3704 =head2 Multiple Values
3706 An C<isl_multi_val> object represents a sequence of zero or more values,
3707 living in a set space.
3709 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3710 using the following function
3712 #include <isl/val.h>
3713 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3714 __isl_take isl_space *space,
3715 __isl_take isl_val_list *list);
3717 The zero multiple value (with value zero for each set dimension)
3718 can be created using the following function.
3720 #include <isl/val.h>
3721 __isl_give isl_multi_val *isl_multi_val_zero(
3722 __isl_take isl_space *space);
3724 Multiple values can be copied and freed using
3726 #include <isl/val.h>
3727 __isl_give isl_multi_val *isl_multi_val_copy(
3728 __isl_keep isl_multi_val *mv);
3729 __isl_null isl_multi_val *isl_multi_val_free(
3730 __isl_take isl_multi_val *mv);
3732 They can be inspected using
3734 #include <isl/val.h>
3735 isl_ctx *isl_multi_val_get_ctx(
3736 __isl_keep isl_multi_val *mv);
3737 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3738 enum isl_dim_type type);
3739 __isl_give isl_val *isl_multi_val_get_val(
3740 __isl_keep isl_multi_val *mv, int pos);
3741 int isl_multi_val_find_dim_by_id(
3742 __isl_keep isl_multi_val *mv,
3743 enum isl_dim_type type, __isl_keep isl_id *id);
3744 __isl_give isl_id *isl_multi_val_get_dim_id(
3745 __isl_keep isl_multi_val *mv,
3746 enum isl_dim_type type, unsigned pos);
3747 const char *isl_multi_val_get_tuple_name(
3748 __isl_keep isl_multi_val *mv,
3749 enum isl_dim_type type);
3750 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3751 enum isl_dim_type type);
3752 __isl_give isl_id *isl_multi_val_get_tuple_id(
3753 __isl_keep isl_multi_val *mv,
3754 enum isl_dim_type type);
3755 int isl_multi_val_range_is_wrapping(
3756 __isl_keep isl_multi_val *mv);
3758 They can be modified using
3760 #include <isl/val.h>
3761 __isl_give isl_multi_val *isl_multi_val_set_val(
3762 __isl_take isl_multi_val *mv, int pos,
3763 __isl_take isl_val *val);
3764 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3765 __isl_take isl_multi_val *mv,
3766 enum isl_dim_type type, unsigned pos, const char *s);
3767 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3768 __isl_take isl_multi_val *mv,
3769 enum isl_dim_type type, unsigned pos,
3770 __isl_take isl_id *id);
3771 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3772 __isl_take isl_multi_val *mv,
3773 enum isl_dim_type type, const char *s);
3774 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3775 __isl_take isl_multi_val *mv,
3776 enum isl_dim_type type, __isl_take isl_id *id);
3777 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3778 __isl_take isl_multi_val *mv,
3779 enum isl_dim_type type);
3780 __isl_give isl_multi_val *isl_multi_val_reset_user(
3781 __isl_take isl_multi_val *mv);
3783 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3784 __isl_take isl_multi_val *mv,
3785 enum isl_dim_type type, unsigned first, unsigned n);
3786 __isl_give isl_multi_val *isl_multi_val_add_dims(
3787 __isl_take isl_multi_val *mv,
3788 enum isl_dim_type type, unsigned n);
3789 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3790 __isl_take isl_multi_val *mv,
3791 enum isl_dim_type type, unsigned first, unsigned n);
3795 #include <isl/val.h>
3796 __isl_give isl_multi_val *isl_multi_val_align_params(
3797 __isl_take isl_multi_val *mv,
3798 __isl_take isl_space *model);
3799 __isl_give isl_multi_val *isl_multi_val_from_range(
3800 __isl_take isl_multi_val *mv);
3801 __isl_give isl_multi_val *isl_multi_val_range_splice(
3802 __isl_take isl_multi_val *mv1, unsigned pos,
3803 __isl_take isl_multi_val *mv2);
3804 __isl_give isl_multi_val *isl_multi_val_range_product(
3805 __isl_take isl_multi_val *mv1,
3806 __isl_take isl_multi_val *mv2);
3807 __isl_give isl_multi_val *
3808 isl_multi_val_range_factor_domain(
3809 __isl_take isl_multi_val *mv);
3810 __isl_give isl_multi_val *
3811 isl_multi_val_range_factor_range(
3812 __isl_take isl_multi_val *mv);
3813 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3814 __isl_take isl_multi_val *mv1,
3815 __isl_take isl_multi_aff *mv2);
3816 __isl_give isl_multi_val *isl_multi_val_product(
3817 __isl_take isl_multi_val *mv1,
3818 __isl_take isl_multi_val *mv2);
3819 __isl_give isl_multi_val *isl_multi_val_add_val(
3820 __isl_take isl_multi_val *mv,
3821 __isl_take isl_val *v);
3822 __isl_give isl_multi_val *isl_multi_val_mod_val(
3823 __isl_take isl_multi_val *mv,
3824 __isl_take isl_val *v);
3825 __isl_give isl_multi_val *isl_multi_val_scale_val(
3826 __isl_take isl_multi_val *mv,
3827 __isl_take isl_val *v);
3828 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3829 __isl_take isl_multi_val *mv1,
3830 __isl_take isl_multi_val *mv2);
3831 __isl_give isl_multi_val *
3832 isl_multi_val_scale_down_multi_val(
3833 __isl_take isl_multi_val *mv1,
3834 __isl_take isl_multi_val *mv2);
3836 A multiple value can be printed using
3838 __isl_give isl_printer *isl_printer_print_multi_val(
3839 __isl_take isl_printer *p,
3840 __isl_keep isl_multi_val *mv);
3844 Vectors can be created, copied and freed using the following functions.
3846 #include <isl/vec.h>
3847 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3849 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3850 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
3852 Note that the elements of a newly created vector may have arbitrary values.
3853 The elements can be changed and inspected using the following functions.
3855 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3856 int isl_vec_size(__isl_keep isl_vec *vec);
3857 __isl_give isl_val *isl_vec_get_element_val(
3858 __isl_keep isl_vec *vec, int pos);
3859 __isl_give isl_vec *isl_vec_set_element_si(
3860 __isl_take isl_vec *vec, int pos, int v);
3861 __isl_give isl_vec *isl_vec_set_element_val(
3862 __isl_take isl_vec *vec, int pos,
3863 __isl_take isl_val *v);
3864 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3866 __isl_give isl_vec *isl_vec_set_val(
3867 __isl_take isl_vec *vec, __isl_take isl_val *v);
3868 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3869 __isl_keep isl_vec *vec2, int pos);
3871 C<isl_vec_get_element> will return a negative value if anything went wrong.
3872 In that case, the value of C<*v> is undefined.
3874 The following function can be used to concatenate two vectors.
3876 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3877 __isl_take isl_vec *vec2);
3881 Matrices can be created, copied and freed using the following functions.
3883 #include <isl/mat.h>
3884 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3885 unsigned n_row, unsigned n_col);
3886 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3887 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
3889 Note that the elements of a newly created matrix may have arbitrary values.
3890 The elements can be changed and inspected using the following functions.
3892 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3893 int isl_mat_rows(__isl_keep isl_mat *mat);
3894 int isl_mat_cols(__isl_keep isl_mat *mat);
3895 __isl_give isl_val *isl_mat_get_element_val(
3896 __isl_keep isl_mat *mat, int row, int col);
3897 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3898 int row, int col, int v);
3899 __isl_give isl_mat *isl_mat_set_element_val(
3900 __isl_take isl_mat *mat, int row, int col,
3901 __isl_take isl_val *v);
3903 C<isl_mat_get_element> will return a negative value if anything went wrong.
3904 In that case, the value of C<*v> is undefined.
3906 The following function can be used to compute the (right) inverse
3907 of a matrix, i.e., a matrix such that the product of the original
3908 and the inverse (in that order) is a multiple of the identity matrix.
3909 The input matrix is assumed to be of full row-rank.
3911 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3913 The following function can be used to compute the (right) kernel
3914 (or null space) of a matrix, i.e., a matrix such that the product of
3915 the original and the kernel (in that order) is the zero matrix.
3917 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3919 =head2 Piecewise Quasi Affine Expressions
3921 The zero quasi affine expression or the quasi affine expression
3922 that is equal to a given value or
3923 a specified dimension on a given domain can be created using
3925 __isl_give isl_aff *isl_aff_zero_on_domain(
3926 __isl_take isl_local_space *ls);
3927 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3928 __isl_take isl_local_space *ls);
3929 __isl_give isl_aff *isl_aff_val_on_domain(
3930 __isl_take isl_local_space *ls,
3931 __isl_take isl_val *val);
3932 __isl_give isl_aff *isl_aff_var_on_domain(
3933 __isl_take isl_local_space *ls,
3934 enum isl_dim_type type, unsigned pos);
3935 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3936 __isl_take isl_local_space *ls,
3937 enum isl_dim_type type, unsigned pos);
3938 __isl_give isl_aff *isl_aff_nan_on_domain(
3939 __isl_take isl_local_space *ls);
3940 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3941 __isl_take isl_local_space *ls);
3943 Note that the space in which the resulting objects live is a map space
3944 with the given space as domain and a one-dimensional range.
3946 An empty piecewise quasi affine expression (one with no cells)
3947 or a piecewise quasi affine expression with a single cell can
3948 be created using the following functions.
3950 #include <isl/aff.h>
3951 __isl_give isl_pw_aff *isl_pw_aff_empty(
3952 __isl_take isl_space *space);
3953 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3954 __isl_take isl_set *set, __isl_take isl_aff *aff);
3955 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3956 __isl_take isl_aff *aff);
3958 A piecewise quasi affine expression that is equal to 1 on a set
3959 and 0 outside the set can be created using the following function.
3961 #include <isl/aff.h>
3962 __isl_give isl_pw_aff *isl_set_indicator_function(
3963 __isl_take isl_set *set);
3965 Quasi affine expressions can be copied and freed using
3967 #include <isl/aff.h>
3968 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3969 __isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff);
3971 __isl_give isl_pw_aff *isl_pw_aff_copy(
3972 __isl_keep isl_pw_aff *pwaff);
3973 __isl_null isl_pw_aff *isl_pw_aff_free(
3974 __isl_take isl_pw_aff *pwaff);
3976 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3977 using the following function. The constraint is required to have
3978 a non-zero coefficient for the specified dimension.
3980 #include <isl/constraint.h>
3981 __isl_give isl_aff *isl_constraint_get_bound(
3982 __isl_keep isl_constraint *constraint,
3983 enum isl_dim_type type, int pos);
3985 The entire affine expression of the constraint can also be extracted
3986 using the following function.
3988 #include <isl/constraint.h>
3989 __isl_give isl_aff *isl_constraint_get_aff(
3990 __isl_keep isl_constraint *constraint);
3992 Conversely, an equality constraint equating
3993 the affine expression to zero or an inequality constraint enforcing
3994 the affine expression to be non-negative, can be constructed using
3996 __isl_give isl_constraint *isl_equality_from_aff(
3997 __isl_take isl_aff *aff);
3998 __isl_give isl_constraint *isl_inequality_from_aff(
3999 __isl_take isl_aff *aff);
4001 The expression can be inspected using
4003 #include <isl/aff.h>
4004 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
4005 int isl_aff_dim(__isl_keep isl_aff *aff,
4006 enum isl_dim_type type);
4007 __isl_give isl_local_space *isl_aff_get_domain_local_space(
4008 __isl_keep isl_aff *aff);
4009 __isl_give isl_local_space *isl_aff_get_local_space(
4010 __isl_keep isl_aff *aff);
4011 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
4012 enum isl_dim_type type, unsigned pos);
4013 const char *isl_pw_aff_get_dim_name(
4014 __isl_keep isl_pw_aff *pa,
4015 enum isl_dim_type type, unsigned pos);
4016 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
4017 enum isl_dim_type type, unsigned pos);
4018 __isl_give isl_id *isl_pw_aff_get_dim_id(
4019 __isl_keep isl_pw_aff *pa,
4020 enum isl_dim_type type, unsigned pos);
4021 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
4022 enum isl_dim_type type);
4023 __isl_give isl_id *isl_pw_aff_get_tuple_id(
4024 __isl_keep isl_pw_aff *pa,
4025 enum isl_dim_type type);
4026 __isl_give isl_val *isl_aff_get_constant_val(
4027 __isl_keep isl_aff *aff);
4028 __isl_give isl_val *isl_aff_get_coefficient_val(
4029 __isl_keep isl_aff *aff,
4030 enum isl_dim_type type, int pos);
4031 __isl_give isl_val *isl_aff_get_denominator_val(
4032 __isl_keep isl_aff *aff);
4033 __isl_give isl_aff *isl_aff_get_div(
4034 __isl_keep isl_aff *aff, int pos);
4036 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
4037 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
4038 int (*fn)(__isl_take isl_set *set,
4039 __isl_take isl_aff *aff,
4040 void *user), void *user);
4042 int isl_aff_is_cst(__isl_keep isl_aff *aff);
4043 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4045 int isl_aff_is_nan(__isl_keep isl_aff *aff);
4046 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
4048 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
4049 enum isl_dim_type type, unsigned first, unsigned n);
4050 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
4051 enum isl_dim_type type, unsigned first, unsigned n);
4053 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
4054 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
4055 enum isl_dim_type type);
4056 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
4058 It can be modified using
4060 #include <isl/aff.h>
4061 __isl_give isl_aff *isl_aff_set_tuple_id(
4062 __isl_take isl_aff *aff,
4063 enum isl_dim_type type, __isl_take isl_id *id);
4064 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
4065 __isl_take isl_pw_aff *pwaff,
4066 enum isl_dim_type type, __isl_take isl_id *id);
4067 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
4068 __isl_take isl_pw_aff *pa,
4069 enum isl_dim_type type);
4070 __isl_give isl_aff *isl_aff_set_dim_name(
4071 __isl_take isl_aff *aff, enum isl_dim_type type,
4072 unsigned pos, const char *s);
4073 __isl_give isl_aff *isl_aff_set_dim_id(
4074 __isl_take isl_aff *aff, enum isl_dim_type type,
4075 unsigned pos, __isl_take isl_id *id);
4076 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
4077 __isl_take isl_pw_aff *pma,
4078 enum isl_dim_type type, unsigned pos,
4079 __isl_take isl_id *id);
4080 __isl_give isl_aff *isl_aff_set_constant_si(
4081 __isl_take isl_aff *aff, int v);
4082 __isl_give isl_aff *isl_aff_set_constant_val(
4083 __isl_take isl_aff *aff, __isl_take isl_val *v);
4084 __isl_give isl_aff *isl_aff_set_coefficient_si(
4085 __isl_take isl_aff *aff,
4086 enum isl_dim_type type, int pos, int v);
4087 __isl_give isl_aff *isl_aff_set_coefficient_val(
4088 __isl_take isl_aff *aff,
4089 enum isl_dim_type type, int pos,
4090 __isl_take isl_val *v);
4092 __isl_give isl_aff *isl_aff_add_constant_si(
4093 __isl_take isl_aff *aff, int v);
4094 __isl_give isl_aff *isl_aff_add_constant_val(
4095 __isl_take isl_aff *aff, __isl_take isl_val *v);
4096 __isl_give isl_aff *isl_aff_add_constant_num_si(
4097 __isl_take isl_aff *aff, int v);
4098 __isl_give isl_aff *isl_aff_add_coefficient_si(
4099 __isl_take isl_aff *aff,
4100 enum isl_dim_type type, int pos, int v);
4101 __isl_give isl_aff *isl_aff_add_coefficient_val(
4102 __isl_take isl_aff *aff,
4103 enum isl_dim_type type, int pos,
4104 __isl_take isl_val *v);
4106 __isl_give isl_aff *isl_aff_insert_dims(
4107 __isl_take isl_aff *aff,
4108 enum isl_dim_type type, unsigned first, unsigned n);
4109 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4110 __isl_take isl_pw_aff *pwaff,
4111 enum isl_dim_type type, unsigned first, unsigned n);
4112 __isl_give isl_aff *isl_aff_add_dims(
4113 __isl_take isl_aff *aff,
4114 enum isl_dim_type type, unsigned n);
4115 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4116 __isl_take isl_pw_aff *pwaff,
4117 enum isl_dim_type type, unsigned n);
4118 __isl_give isl_aff *isl_aff_drop_dims(
4119 __isl_take isl_aff *aff,
4120 enum isl_dim_type type, unsigned first, unsigned n);
4121 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4122 __isl_take isl_pw_aff *pwaff,
4123 enum isl_dim_type type, unsigned first, unsigned n);
4124 __isl_give isl_aff *isl_aff_move_dims(
4125 __isl_take isl_aff *aff,
4126 enum isl_dim_type dst_type, unsigned dst_pos,
4127 enum isl_dim_type src_type, unsigned src_pos,
4129 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4130 __isl_take isl_pw_aff *pa,
4131 enum isl_dim_type dst_type, unsigned dst_pos,
4132 enum isl_dim_type src_type, unsigned src_pos,
4135 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
4136 set the I<numerator> of the constant or coefficient, while
4137 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
4138 the constant or coefficient as a whole.
4139 The C<add_constant> and C<add_coefficient> functions add an integer
4140 or rational value to
4141 the possibly rational constant or coefficient.
4142 The C<add_constant_num> functions add an integer value to
4145 To check whether an affine expressions is obviously zero
4146 or (obviously) equal to some other affine expression, use
4148 #include <isl/aff.h>
4149 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
4150 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
4151 __isl_keep isl_aff *aff2);
4152 int isl_pw_aff_plain_is_equal(
4153 __isl_keep isl_pw_aff *pwaff1,
4154 __isl_keep isl_pw_aff *pwaff2);
4155 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
4156 __isl_keep isl_pw_aff *pa2);
4157 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4158 __isl_keep isl_pw_aff *pa2);
4160 The function C<isl_pw_aff_plain_cmp> can be used to sort
4161 C<isl_pw_aff>s. The order is not strictly defined.
4162 The current order sorts expressions that only involve
4163 earlier dimensions before those that involve later dimensions.
4167 #include <isl/aff.h>
4168 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
4169 __isl_take isl_aff *aff2);
4170 __isl_give isl_pw_aff *isl_pw_aff_add(
4171 __isl_take isl_pw_aff *pwaff1,
4172 __isl_take isl_pw_aff *pwaff2);
4173 __isl_give isl_pw_aff *isl_pw_aff_min(
4174 __isl_take isl_pw_aff *pwaff1,
4175 __isl_take isl_pw_aff *pwaff2);
4176 __isl_give isl_pw_aff *isl_pw_aff_max(
4177 __isl_take isl_pw_aff *pwaff1,
4178 __isl_take isl_pw_aff *pwaff2);
4179 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4180 __isl_take isl_aff *aff2);
4181 __isl_give isl_pw_aff *isl_pw_aff_sub(
4182 __isl_take isl_pw_aff *pwaff1,
4183 __isl_take isl_pw_aff *pwaff2);
4184 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4185 __isl_give isl_pw_aff *isl_pw_aff_neg(
4186 __isl_take isl_pw_aff *pwaff);
4187 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4188 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4189 __isl_take isl_pw_aff *pwaff);
4190 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4191 __isl_give isl_pw_aff *isl_pw_aff_floor(
4192 __isl_take isl_pw_aff *pwaff);
4193 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4194 __isl_take isl_val *mod);
4195 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4196 __isl_take isl_pw_aff *pa,
4197 __isl_take isl_val *mod);
4198 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4199 __isl_take isl_val *v);
4200 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4201 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4202 __isl_give isl_aff *isl_aff_scale_down_ui(
4203 __isl_take isl_aff *aff, unsigned f);
4204 __isl_give isl_aff *isl_aff_scale_down_val(
4205 __isl_take isl_aff *aff, __isl_take isl_val *v);
4206 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4207 __isl_take isl_pw_aff *pa,
4208 __isl_take isl_val *f);
4210 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4211 __isl_take isl_pw_aff_list *list);
4212 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4213 __isl_take isl_pw_aff_list *list);
4215 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4216 __isl_take isl_pw_aff *pwqp);
4218 __isl_give isl_aff *isl_aff_align_params(
4219 __isl_take isl_aff *aff,
4220 __isl_take isl_space *model);
4221 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4222 __isl_take isl_pw_aff *pwaff,
4223 __isl_take isl_space *model);
4225 __isl_give isl_aff *isl_aff_project_domain_on_params(
4226 __isl_take isl_aff *aff);
4227 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4228 __isl_take isl_pw_aff *pwa);
4230 __isl_give isl_aff *isl_aff_gist_params(
4231 __isl_take isl_aff *aff,
4232 __isl_take isl_set *context);
4233 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4234 __isl_take isl_set *context);
4235 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4236 __isl_take isl_pw_aff *pwaff,
4237 __isl_take isl_set *context);
4238 __isl_give isl_pw_aff *isl_pw_aff_gist(
4239 __isl_take isl_pw_aff *pwaff,
4240 __isl_take isl_set *context);
4242 __isl_give isl_set *isl_pw_aff_domain(
4243 __isl_take isl_pw_aff *pwaff);
4244 __isl_give isl_set *isl_pw_aff_params(
4245 __isl_take isl_pw_aff *pwa);
4246 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4247 __isl_take isl_pw_aff *pa,
4248 __isl_take isl_set *set);
4249 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4250 __isl_take isl_pw_aff *pa,
4251 __isl_take isl_set *set);
4253 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4254 __isl_take isl_aff *aff2);
4255 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4256 __isl_take isl_aff *aff2);
4257 __isl_give isl_pw_aff *isl_pw_aff_mul(
4258 __isl_take isl_pw_aff *pwaff1,
4259 __isl_take isl_pw_aff *pwaff2);
4260 __isl_give isl_pw_aff *isl_pw_aff_div(
4261 __isl_take isl_pw_aff *pa1,
4262 __isl_take isl_pw_aff *pa2);
4263 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4264 __isl_take isl_pw_aff *pa1,
4265 __isl_take isl_pw_aff *pa2);
4266 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4267 __isl_take isl_pw_aff *pa1,
4268 __isl_take isl_pw_aff *pa2);
4270 When multiplying two affine expressions, at least one of the two needs
4271 to be a constant. Similarly, when dividing an affine expression by another,
4272 the second expression needs to be a constant.
4273 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4274 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4277 #include <isl/aff.h>
4278 __isl_give isl_aff *isl_aff_pullback_aff(
4279 __isl_take isl_aff *aff1,
4280 __isl_take isl_aff *aff2);
4281 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4282 __isl_take isl_aff *aff,
4283 __isl_take isl_multi_aff *ma);
4284 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4285 __isl_take isl_pw_aff *pa,
4286 __isl_take isl_multi_aff *ma);
4287 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4288 __isl_take isl_pw_aff *pa,
4289 __isl_take isl_pw_multi_aff *pma);
4290 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4291 __isl_take isl_pw_aff *pa,
4292 __isl_take isl_multi_pw_aff *mpa);
4294 These functions precompose the input expression by the given
4295 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4296 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4297 into the (piecewise) affine expression.
4298 Objects of type C<isl_multi_aff> are described in
4299 L</"Piecewise Multiple Quasi Affine Expressions">.
4301 #include <isl/aff.h>
4302 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4303 __isl_take isl_aff *aff);
4304 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4305 __isl_take isl_aff *aff);
4306 __isl_give isl_basic_set *isl_aff_le_basic_set(
4307 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4308 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4309 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4310 __isl_give isl_set *isl_pw_aff_eq_set(
4311 __isl_take isl_pw_aff *pwaff1,
4312 __isl_take isl_pw_aff *pwaff2);
4313 __isl_give isl_set *isl_pw_aff_ne_set(
4314 __isl_take isl_pw_aff *pwaff1,
4315 __isl_take isl_pw_aff *pwaff2);
4316 __isl_give isl_set *isl_pw_aff_le_set(
4317 __isl_take isl_pw_aff *pwaff1,
4318 __isl_take isl_pw_aff *pwaff2);
4319 __isl_give isl_set *isl_pw_aff_lt_set(
4320 __isl_take isl_pw_aff *pwaff1,
4321 __isl_take isl_pw_aff *pwaff2);
4322 __isl_give isl_set *isl_pw_aff_ge_set(
4323 __isl_take isl_pw_aff *pwaff1,
4324 __isl_take isl_pw_aff *pwaff2);
4325 __isl_give isl_set *isl_pw_aff_gt_set(
4326 __isl_take isl_pw_aff *pwaff1,
4327 __isl_take isl_pw_aff *pwaff2);
4329 __isl_give isl_set *isl_pw_aff_list_eq_set(
4330 __isl_take isl_pw_aff_list *list1,
4331 __isl_take isl_pw_aff_list *list2);
4332 __isl_give isl_set *isl_pw_aff_list_ne_set(
4333 __isl_take isl_pw_aff_list *list1,
4334 __isl_take isl_pw_aff_list *list2);
4335 __isl_give isl_set *isl_pw_aff_list_le_set(
4336 __isl_take isl_pw_aff_list *list1,
4337 __isl_take isl_pw_aff_list *list2);
4338 __isl_give isl_set *isl_pw_aff_list_lt_set(
4339 __isl_take isl_pw_aff_list *list1,
4340 __isl_take isl_pw_aff_list *list2);
4341 __isl_give isl_set *isl_pw_aff_list_ge_set(
4342 __isl_take isl_pw_aff_list *list1,
4343 __isl_take isl_pw_aff_list *list2);
4344 __isl_give isl_set *isl_pw_aff_list_gt_set(
4345 __isl_take isl_pw_aff_list *list1,
4346 __isl_take isl_pw_aff_list *list2);
4348 The function C<isl_aff_neg_basic_set> returns a basic set
4349 containing those elements in the domain space
4350 of C<aff> where C<aff> is negative.
4351 The function C<isl_aff_ge_basic_set> returns a basic set
4352 containing those elements in the shared space
4353 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4354 The function C<isl_pw_aff_ge_set> returns a set
4355 containing those elements in the shared domain
4356 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4357 The functions operating on C<isl_pw_aff_list> apply the corresponding
4358 C<isl_pw_aff> function to each pair of elements in the two lists.
4360 #include <isl/aff.h>
4361 __isl_give isl_set *isl_pw_aff_nonneg_set(
4362 __isl_take isl_pw_aff *pwaff);
4363 __isl_give isl_set *isl_pw_aff_zero_set(
4364 __isl_take isl_pw_aff *pwaff);
4365 __isl_give isl_set *isl_pw_aff_non_zero_set(
4366 __isl_take isl_pw_aff *pwaff);
4368 The function C<isl_pw_aff_nonneg_set> returns a set
4369 containing those elements in the domain
4370 of C<pwaff> where C<pwaff> is non-negative.
4372 #include <isl/aff.h>
4373 __isl_give isl_pw_aff *isl_pw_aff_cond(
4374 __isl_take isl_pw_aff *cond,
4375 __isl_take isl_pw_aff *pwaff_true,
4376 __isl_take isl_pw_aff *pwaff_false);
4378 The function C<isl_pw_aff_cond> performs a conditional operator
4379 and returns an expression that is equal to C<pwaff_true>
4380 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4381 where C<cond> is zero.
4383 #include <isl/aff.h>
4384 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4385 __isl_take isl_pw_aff *pwaff1,
4386 __isl_take isl_pw_aff *pwaff2);
4387 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4388 __isl_take isl_pw_aff *pwaff1,
4389 __isl_take isl_pw_aff *pwaff2);
4390 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4391 __isl_take isl_pw_aff *pwaff1,
4392 __isl_take isl_pw_aff *pwaff2);
4394 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4395 expression with a domain that is the union of those of C<pwaff1> and
4396 C<pwaff2> and such that on each cell, the quasi-affine expression is
4397 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4398 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4399 associated expression is the defined one.
4401 An expression can be read from input using
4403 #include <isl/aff.h>
4404 __isl_give isl_aff *isl_aff_read_from_str(
4405 isl_ctx *ctx, const char *str);
4406 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4407 isl_ctx *ctx, const char *str);
4409 An expression can be printed using
4411 #include <isl/aff.h>
4412 __isl_give isl_printer *isl_printer_print_aff(
4413 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4415 __isl_give isl_printer *isl_printer_print_pw_aff(
4416 __isl_take isl_printer *p,
4417 __isl_keep isl_pw_aff *pwaff);
4419 =head2 Piecewise Multiple Quasi Affine Expressions
4421 An C<isl_multi_aff> object represents a sequence of
4422 zero or more affine expressions, all defined on the same domain space.
4423 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4424 zero or more piecewise affine expressions.
4426 An C<isl_multi_aff> can be constructed from a single
4427 C<isl_aff> or an C<isl_aff_list> using the
4428 following functions. Similarly for C<isl_multi_pw_aff>
4429 and C<isl_pw_multi_aff>.
4431 #include <isl/aff.h>
4432 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4433 __isl_take isl_aff *aff);
4434 __isl_give isl_multi_pw_aff *
4435 isl_multi_pw_aff_from_multi_aff(
4436 __isl_take isl_multi_aff *ma);
4437 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4438 __isl_take isl_pw_aff *pa);
4439 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4440 __isl_take isl_pw_aff *pa);
4441 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4442 __isl_take isl_space *space,
4443 __isl_take isl_aff_list *list);
4445 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4446 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4447 Note however that the domain
4448 of the result is the intersection of the domains of the input.
4449 The reverse conversion is exact.
4451 #include <isl/aff.h>
4452 __isl_give isl_pw_multi_aff *
4453 isl_pw_multi_aff_from_multi_pw_aff(
4454 __isl_take isl_multi_pw_aff *mpa);
4455 __isl_give isl_multi_pw_aff *
4456 isl_multi_pw_aff_from_pw_multi_aff(
4457 __isl_take isl_pw_multi_aff *pma);
4459 An empty piecewise multiple quasi affine expression (one with no cells),
4460 the zero piecewise multiple quasi affine expression (with value zero
4461 for each output dimension),
4462 a piecewise multiple quasi affine expression with a single cell (with
4463 either a universe or a specified domain) or
4464 a zero-dimensional piecewise multiple quasi affine expression
4466 can be created using the following functions.
4468 #include <isl/aff.h>
4469 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4470 __isl_take isl_space *space);
4471 __isl_give isl_multi_aff *isl_multi_aff_zero(
4472 __isl_take isl_space *space);
4473 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4474 __isl_take isl_space *space);
4475 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4476 __isl_take isl_space *space);
4477 __isl_give isl_multi_aff *isl_multi_aff_identity(
4478 __isl_take isl_space *space);
4479 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4480 __isl_take isl_space *space);
4481 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4482 __isl_take isl_space *space);
4483 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4484 __isl_take isl_space *space);
4485 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4486 __isl_take isl_space *space);
4487 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4488 __isl_take isl_space *space,
4489 enum isl_dim_type type,
4490 unsigned first, unsigned n);
4491 __isl_give isl_pw_multi_aff *
4492 isl_pw_multi_aff_project_out_map(
4493 __isl_take isl_space *space,
4494 enum isl_dim_type type,
4495 unsigned first, unsigned n);
4496 __isl_give isl_pw_multi_aff *
4497 isl_pw_multi_aff_from_multi_aff(
4498 __isl_take isl_multi_aff *ma);
4499 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4500 __isl_take isl_set *set,
4501 __isl_take isl_multi_aff *maff);
4502 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4503 __isl_take isl_set *set);
4505 __isl_give isl_union_pw_multi_aff *
4506 isl_union_pw_multi_aff_empty(
4507 __isl_take isl_space *space);
4508 __isl_give isl_union_pw_multi_aff *
4509 isl_union_pw_multi_aff_add_pw_multi_aff(
4510 __isl_take isl_union_pw_multi_aff *upma,
4511 __isl_take isl_pw_multi_aff *pma);
4512 __isl_give isl_union_pw_multi_aff *
4513 isl_union_pw_multi_aff_from_domain(
4514 __isl_take isl_union_set *uset);
4516 A piecewise multiple quasi affine expression can also be initialized
4517 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4518 and the C<isl_map> is single-valued.
4519 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4520 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4522 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4523 __isl_take isl_set *set);
4524 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4525 __isl_take isl_map *map);
4527 __isl_give isl_union_pw_multi_aff *
4528 isl_union_pw_multi_aff_from_union_set(
4529 __isl_take isl_union_set *uset);
4530 __isl_give isl_union_pw_multi_aff *
4531 isl_union_pw_multi_aff_from_union_map(
4532 __isl_take isl_union_map *umap);
4534 Multiple quasi affine expressions can be copied and freed using
4536 #include <isl/aff.h>
4537 __isl_give isl_multi_aff *isl_multi_aff_copy(
4538 __isl_keep isl_multi_aff *maff);
4539 __isl_null isl_multi_aff *isl_multi_aff_free(
4540 __isl_take isl_multi_aff *maff);
4542 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4543 __isl_keep isl_pw_multi_aff *pma);
4544 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
4545 __isl_take isl_pw_multi_aff *pma);
4547 __isl_give isl_union_pw_multi_aff *
4548 isl_union_pw_multi_aff_copy(
4549 __isl_keep isl_union_pw_multi_aff *upma);
4550 __isl_null isl_union_pw_multi_aff *
4551 isl_union_pw_multi_aff_free(
4552 __isl_take isl_union_pw_multi_aff *upma);
4554 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4555 __isl_keep isl_multi_pw_aff *mpa);
4556 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
4557 __isl_take isl_multi_pw_aff *mpa);
4559 The expression can be inspected using
4561 #include <isl/aff.h>
4562 isl_ctx *isl_multi_aff_get_ctx(
4563 __isl_keep isl_multi_aff *maff);
4564 isl_ctx *isl_pw_multi_aff_get_ctx(
4565 __isl_keep isl_pw_multi_aff *pma);
4566 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4567 __isl_keep isl_union_pw_multi_aff *upma);
4568 isl_ctx *isl_multi_pw_aff_get_ctx(
4569 __isl_keep isl_multi_pw_aff *mpa);
4571 int isl_multi_aff_involves_dims(
4572 __isl_keep isl_multi_aff *ma,
4573 enum isl_dim_type type, unsigned first, unsigned n);
4574 int isl_multi_pw_aff_involves_dims(
4575 __isl_keep isl_multi_pw_aff *mpa,
4576 enum isl_dim_type type, unsigned first, unsigned n);
4578 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4579 enum isl_dim_type type);
4580 unsigned isl_pw_multi_aff_dim(
4581 __isl_keep isl_pw_multi_aff *pma,
4582 enum isl_dim_type type);
4583 unsigned isl_multi_pw_aff_dim(
4584 __isl_keep isl_multi_pw_aff *mpa,
4585 enum isl_dim_type type);
4586 __isl_give isl_aff *isl_multi_aff_get_aff(
4587 __isl_keep isl_multi_aff *multi, int pos);
4588 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4589 __isl_keep isl_pw_multi_aff *pma, int pos);
4590 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4591 __isl_keep isl_multi_pw_aff *mpa, int pos);
4592 int isl_multi_aff_find_dim_by_id(
4593 __isl_keep isl_multi_aff *ma,
4594 enum isl_dim_type type, __isl_keep isl_id *id);
4595 int isl_multi_pw_aff_find_dim_by_id(
4596 __isl_keep isl_multi_pw_aff *mpa,
4597 enum isl_dim_type type, __isl_keep isl_id *id);
4598 const char *isl_pw_multi_aff_get_dim_name(
4599 __isl_keep isl_pw_multi_aff *pma,
4600 enum isl_dim_type type, unsigned pos);
4601 __isl_give isl_id *isl_multi_aff_get_dim_id(
4602 __isl_keep isl_multi_aff *ma,
4603 enum isl_dim_type type, unsigned pos);
4604 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4605 __isl_keep isl_pw_multi_aff *pma,
4606 enum isl_dim_type type, unsigned pos);
4607 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4608 __isl_keep isl_multi_pw_aff *mpa,
4609 enum isl_dim_type type, unsigned pos);
4610 const char *isl_multi_aff_get_tuple_name(
4611 __isl_keep isl_multi_aff *multi,
4612 enum isl_dim_type type);
4613 int isl_pw_multi_aff_has_tuple_name(
4614 __isl_keep isl_pw_multi_aff *pma,
4615 enum isl_dim_type type);
4616 const char *isl_pw_multi_aff_get_tuple_name(
4617 __isl_keep isl_pw_multi_aff *pma,
4618 enum isl_dim_type type);
4619 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4620 enum isl_dim_type type);
4621 int isl_pw_multi_aff_has_tuple_id(
4622 __isl_keep isl_pw_multi_aff *pma,
4623 enum isl_dim_type type);
4624 int isl_multi_pw_aff_has_tuple_id(
4625 __isl_keep isl_multi_pw_aff *mpa,
4626 enum isl_dim_type type);
4627 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4628 __isl_keep isl_multi_aff *ma,
4629 enum isl_dim_type type);
4630 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4631 __isl_keep isl_pw_multi_aff *pma,
4632 enum isl_dim_type type);
4633 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4634 __isl_keep isl_multi_pw_aff *mpa,
4635 enum isl_dim_type type);
4636 int isl_multi_aff_range_is_wrapping(
4637 __isl_keep isl_multi_aff *ma);
4638 int isl_multi_pw_aff_range_is_wrapping(
4639 __isl_keep isl_multi_pw_aff *mpa);
4641 int isl_pw_multi_aff_foreach_piece(
4642 __isl_keep isl_pw_multi_aff *pma,
4643 int (*fn)(__isl_take isl_set *set,
4644 __isl_take isl_multi_aff *maff,
4645 void *user), void *user);
4647 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4648 __isl_keep isl_union_pw_multi_aff *upma,
4649 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4650 void *user), void *user);
4652 It can be modified using
4654 #include <isl/aff.h>
4655 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4656 __isl_take isl_multi_aff *multi, int pos,
4657 __isl_take isl_aff *aff);
4658 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4659 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4660 __isl_take isl_pw_aff *pa);
4661 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4662 __isl_take isl_multi_aff *maff,
4663 enum isl_dim_type type, unsigned pos, const char *s);
4664 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4665 __isl_take isl_multi_aff *maff,
4666 enum isl_dim_type type, unsigned pos,
4667 __isl_take isl_id *id);
4668 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4669 __isl_take isl_multi_aff *maff,
4670 enum isl_dim_type type, const char *s);
4671 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4672 __isl_take isl_multi_aff *maff,
4673 enum isl_dim_type type, __isl_take isl_id *id);
4674 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4675 __isl_take isl_pw_multi_aff *pma,
4676 enum isl_dim_type type, __isl_take isl_id *id);
4677 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4678 __isl_take isl_multi_aff *ma,
4679 enum isl_dim_type type);
4680 __isl_give isl_multi_pw_aff *
4681 isl_multi_pw_aff_reset_tuple_id(
4682 __isl_take isl_multi_pw_aff *mpa,
4683 enum isl_dim_type type);
4684 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4685 __isl_take isl_multi_aff *ma);
4686 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4687 __isl_take isl_multi_pw_aff *mpa);
4689 __isl_give isl_multi_pw_aff *
4690 isl_multi_pw_aff_set_dim_name(
4691 __isl_take isl_multi_pw_aff *mpa,
4692 enum isl_dim_type type, unsigned pos, const char *s);
4693 __isl_give isl_multi_pw_aff *
4694 isl_multi_pw_aff_set_dim_id(
4695 __isl_take isl_multi_pw_aff *mpa,
4696 enum isl_dim_type type, unsigned pos,
4697 __isl_take isl_id *id);
4698 __isl_give isl_multi_pw_aff *
4699 isl_multi_pw_aff_set_tuple_name(
4700 __isl_take isl_multi_pw_aff *mpa,
4701 enum isl_dim_type type, const char *s);
4703 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4704 __isl_take isl_multi_aff *ma);
4706 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4707 __isl_take isl_multi_aff *ma,
4708 enum isl_dim_type type, unsigned first, unsigned n);
4709 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4710 __isl_take isl_multi_aff *ma,
4711 enum isl_dim_type type, unsigned n);
4712 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4713 __isl_take isl_multi_aff *maff,
4714 enum isl_dim_type type, unsigned first, unsigned n);
4715 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4716 __isl_take isl_pw_multi_aff *pma,
4717 enum isl_dim_type type, unsigned first, unsigned n);
4719 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4720 __isl_take isl_multi_pw_aff *mpa,
4721 enum isl_dim_type type, unsigned first, unsigned n);
4722 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4723 __isl_take isl_multi_pw_aff *mpa,
4724 enum isl_dim_type type, unsigned n);
4725 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4726 __isl_take isl_multi_pw_aff *pma,
4727 enum isl_dim_type dst_type, unsigned dst_pos,
4728 enum isl_dim_type src_type, unsigned src_pos,
4731 To check whether two multiple affine expressions are
4732 (obviously) equal to each other, use
4734 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4735 __isl_keep isl_multi_aff *maff2);
4736 int isl_pw_multi_aff_plain_is_equal(
4737 __isl_keep isl_pw_multi_aff *pma1,
4738 __isl_keep isl_pw_multi_aff *pma2);
4739 int isl_multi_pw_aff_plain_is_equal(
4740 __isl_keep isl_multi_pw_aff *mpa1,
4741 __isl_keep isl_multi_pw_aff *mpa2);
4742 int isl_multi_pw_aff_is_equal(
4743 __isl_keep isl_multi_pw_aff *mpa1,
4744 __isl_keep isl_multi_pw_aff *mpa2);
4748 #include <isl/aff.h>
4749 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4750 __isl_take isl_pw_multi_aff *pma1,
4751 __isl_take isl_pw_multi_aff *pma2);
4752 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4753 __isl_take isl_pw_multi_aff *pma1,
4754 __isl_take isl_pw_multi_aff *pma2);
4755 __isl_give isl_multi_aff *isl_multi_aff_floor(
4756 __isl_take isl_multi_aff *ma);
4757 __isl_give isl_multi_aff *isl_multi_aff_add(
4758 __isl_take isl_multi_aff *maff1,
4759 __isl_take isl_multi_aff *maff2);
4760 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4761 __isl_take isl_pw_multi_aff *pma1,
4762 __isl_take isl_pw_multi_aff *pma2);
4763 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4764 __isl_take isl_union_pw_multi_aff *upma1,
4765 __isl_take isl_union_pw_multi_aff *upma2);
4766 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4767 __isl_take isl_pw_multi_aff *pma1,
4768 __isl_take isl_pw_multi_aff *pma2);
4769 __isl_give isl_multi_aff *isl_multi_aff_sub(
4770 __isl_take isl_multi_aff *ma1,
4771 __isl_take isl_multi_aff *ma2);
4772 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4773 __isl_take isl_pw_multi_aff *pma1,
4774 __isl_take isl_pw_multi_aff *pma2);
4775 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4776 __isl_take isl_union_pw_multi_aff *upma1,
4777 __isl_take isl_union_pw_multi_aff *upma2);
4779 C<isl_multi_aff_sub> subtracts the second argument from the first.
4781 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4782 __isl_take isl_multi_aff *ma,
4783 __isl_take isl_val *v);
4784 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4785 __isl_take isl_pw_multi_aff *pma,
4786 __isl_take isl_val *v);
4787 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4788 __isl_take isl_multi_pw_aff *mpa,
4789 __isl_take isl_val *v);
4790 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4791 __isl_take isl_multi_aff *ma,
4792 __isl_take isl_multi_val *mv);
4793 __isl_give isl_pw_multi_aff *
4794 isl_pw_multi_aff_scale_multi_val(
4795 __isl_take isl_pw_multi_aff *pma,
4796 __isl_take isl_multi_val *mv);
4797 __isl_give isl_multi_pw_aff *
4798 isl_multi_pw_aff_scale_multi_val(
4799 __isl_take isl_multi_pw_aff *mpa,
4800 __isl_take isl_multi_val *mv);
4801 __isl_give isl_union_pw_multi_aff *
4802 isl_union_pw_multi_aff_scale_multi_val(
4803 __isl_take isl_union_pw_multi_aff *upma,
4804 __isl_take isl_multi_val *mv);
4805 __isl_give isl_multi_aff *
4806 isl_multi_aff_scale_down_multi_val(
4807 __isl_take isl_multi_aff *ma,
4808 __isl_take isl_multi_val *mv);
4809 __isl_give isl_multi_pw_aff *
4810 isl_multi_pw_aff_scale_down_multi_val(
4811 __isl_take isl_multi_pw_aff *mpa,
4812 __isl_take isl_multi_val *mv);
4814 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4815 by the corresponding elements of C<mv>.
4817 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4818 __isl_take isl_pw_multi_aff *pma,
4819 enum isl_dim_type type, unsigned pos, int value);
4820 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4821 __isl_take isl_pw_multi_aff *pma,
4822 __isl_take isl_set *set);
4823 __isl_give isl_set *isl_multi_pw_aff_domain(
4824 __isl_take isl_multi_pw_aff *mpa);
4825 __isl_give isl_multi_pw_aff *
4826 isl_multi_pw_aff_intersect_params(
4827 __isl_take isl_multi_pw_aff *mpa,
4828 __isl_take isl_set *set);
4829 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4830 __isl_take isl_pw_multi_aff *pma,
4831 __isl_take isl_set *set);
4832 __isl_give isl_multi_pw_aff *
4833 isl_multi_pw_aff_intersect_domain(
4834 __isl_take isl_multi_pw_aff *mpa,
4835 __isl_take isl_set *domain);
4836 __isl_give isl_union_pw_multi_aff *
4837 isl_union_pw_multi_aff_intersect_domain(
4838 __isl_take isl_union_pw_multi_aff *upma,
4839 __isl_take isl_union_set *uset);
4840 __isl_give isl_multi_aff *isl_multi_aff_lift(
4841 __isl_take isl_multi_aff *maff,
4842 __isl_give isl_local_space **ls);
4843 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4844 __isl_take isl_pw_multi_aff *pma);
4845 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4846 __isl_take isl_multi_pw_aff *mpa);
4847 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4848 __isl_take isl_multi_aff *multi,
4849 __isl_take isl_space *model);
4850 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4851 __isl_take isl_pw_multi_aff *pma,
4852 __isl_take isl_space *model);
4853 __isl_give isl_union_pw_multi_aff *
4854 isl_union_pw_multi_aff_align_params(
4855 __isl_take isl_union_pw_multi_aff *upma,
4856 __isl_take isl_space *model);
4857 __isl_give isl_pw_multi_aff *
4858 isl_pw_multi_aff_project_domain_on_params(
4859 __isl_take isl_pw_multi_aff *pma);
4860 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4861 __isl_take isl_multi_aff *maff,
4862 __isl_take isl_set *context);
4863 __isl_give isl_multi_aff *isl_multi_aff_gist(
4864 __isl_take isl_multi_aff *maff,
4865 __isl_take isl_set *context);
4866 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4867 __isl_take isl_pw_multi_aff *pma,
4868 __isl_take isl_set *set);
4869 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4870 __isl_take isl_pw_multi_aff *pma,
4871 __isl_take isl_set *set);
4872 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4873 __isl_take isl_multi_pw_aff *mpa,
4874 __isl_take isl_set *set);
4875 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4876 __isl_take isl_multi_pw_aff *mpa,
4877 __isl_take isl_set *set);
4878 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4879 __isl_take isl_multi_aff *ma);
4880 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4881 __isl_take isl_multi_pw_aff *mpa);
4882 __isl_give isl_set *isl_pw_multi_aff_domain(
4883 __isl_take isl_pw_multi_aff *pma);
4884 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4885 __isl_take isl_union_pw_multi_aff *upma);
4886 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4887 __isl_take isl_multi_aff *ma1, unsigned pos,
4888 __isl_take isl_multi_aff *ma2);
4889 __isl_give isl_multi_aff *isl_multi_aff_splice(
4890 __isl_take isl_multi_aff *ma1,
4891 unsigned in_pos, unsigned out_pos,
4892 __isl_take isl_multi_aff *ma2);
4893 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4894 __isl_take isl_multi_aff *ma1,
4895 __isl_take isl_multi_aff *ma2);
4896 __isl_give isl_multi_aff *
4897 isl_multi_aff_range_factor_domain(
4898 __isl_take isl_multi_aff *ma);
4899 __isl_give isl_multi_aff *
4900 isl_multi_aff_range_factor_range(
4901 __isl_take isl_multi_aff *ma);
4902 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4903 __isl_take isl_multi_aff *ma1,
4904 __isl_take isl_multi_aff *ma2);
4905 __isl_give isl_multi_aff *isl_multi_aff_product(
4906 __isl_take isl_multi_aff *ma1,
4907 __isl_take isl_multi_aff *ma2);
4908 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4909 __isl_take isl_multi_pw_aff *mpa1,
4910 __isl_take isl_multi_pw_aff *mpa2);
4911 __isl_give isl_pw_multi_aff *
4912 isl_pw_multi_aff_range_product(
4913 __isl_take isl_pw_multi_aff *pma1,
4914 __isl_take isl_pw_multi_aff *pma2);
4915 __isl_give isl_multi_pw_aff *
4916 isl_multi_pw_aff_range_factor_domain(
4917 __isl_take isl_multi_pw_aff *mpa);
4918 __isl_give isl_multi_pw_aff *
4919 isl_multi_pw_aff_range_factor_range(
4920 __isl_take isl_multi_pw_aff *mpa);
4921 __isl_give isl_pw_multi_aff *
4922 isl_pw_multi_aff_flat_range_product(
4923 __isl_take isl_pw_multi_aff *pma1,
4924 __isl_take isl_pw_multi_aff *pma2);
4925 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4926 __isl_take isl_pw_multi_aff *pma1,
4927 __isl_take isl_pw_multi_aff *pma2);
4928 __isl_give isl_union_pw_multi_aff *
4929 isl_union_pw_multi_aff_flat_range_product(
4930 __isl_take isl_union_pw_multi_aff *upma1,
4931 __isl_take isl_union_pw_multi_aff *upma2);
4932 __isl_give isl_multi_pw_aff *
4933 isl_multi_pw_aff_range_splice(
4934 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4935 __isl_take isl_multi_pw_aff *mpa2);
4936 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4937 __isl_take isl_multi_pw_aff *mpa1,
4938 unsigned in_pos, unsigned out_pos,
4939 __isl_take isl_multi_pw_aff *mpa2);
4940 __isl_give isl_multi_pw_aff *
4941 isl_multi_pw_aff_range_product(
4942 __isl_take isl_multi_pw_aff *mpa1,
4943 __isl_take isl_multi_pw_aff *mpa2);
4944 __isl_give isl_multi_pw_aff *
4945 isl_multi_pw_aff_flat_range_product(
4946 __isl_take isl_multi_pw_aff *mpa1,
4947 __isl_take isl_multi_pw_aff *mpa2);
4949 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4950 then it is assigned the local space that lies at the basis of
4951 the lifting applied.
4953 #include <isl/aff.h>
4954 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4955 __isl_take isl_multi_aff *ma1,
4956 __isl_take isl_multi_aff *ma2);
4957 __isl_give isl_pw_multi_aff *
4958 isl_pw_multi_aff_pullback_multi_aff(
4959 __isl_take isl_pw_multi_aff *pma,
4960 __isl_take isl_multi_aff *ma);
4961 __isl_give isl_multi_pw_aff *
4962 isl_multi_pw_aff_pullback_multi_aff(
4963 __isl_take isl_multi_pw_aff *mpa,
4964 __isl_take isl_multi_aff *ma);
4965 __isl_give isl_pw_multi_aff *
4966 isl_pw_multi_aff_pullback_pw_multi_aff(
4967 __isl_take isl_pw_multi_aff *pma1,
4968 __isl_take isl_pw_multi_aff *pma2);
4969 __isl_give isl_multi_pw_aff *
4970 isl_multi_pw_aff_pullback_pw_multi_aff(
4971 __isl_take isl_multi_pw_aff *mpa,
4972 __isl_take isl_pw_multi_aff *pma);
4973 __isl_give isl_multi_pw_aff *
4974 isl_multi_pw_aff_pullback_multi_pw_aff(
4975 __isl_take isl_multi_pw_aff *mpa1,
4976 __isl_take isl_multi_pw_aff *mpa2);
4978 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4979 In other words, C<ma2> is plugged
4982 __isl_give isl_set *isl_multi_aff_lex_le_set(
4983 __isl_take isl_multi_aff *ma1,
4984 __isl_take isl_multi_aff *ma2);
4985 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4986 __isl_take isl_multi_aff *ma1,
4987 __isl_take isl_multi_aff *ma2);
4989 The function C<isl_multi_aff_lex_le_set> returns a set
4990 containing those elements in the shared domain space
4991 where C<ma1> is lexicographically smaller than or
4994 An expression can be read from input using
4996 #include <isl/aff.h>
4997 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4998 isl_ctx *ctx, const char *str);
4999 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
5000 isl_ctx *ctx, const char *str);
5001 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
5002 isl_ctx *ctx, const char *str);
5003 __isl_give isl_union_pw_multi_aff *
5004 isl_union_pw_multi_aff_read_from_str(
5005 isl_ctx *ctx, const char *str);
5007 An expression can be printed using
5009 #include <isl/aff.h>
5010 __isl_give isl_printer *isl_printer_print_multi_aff(
5011 __isl_take isl_printer *p,
5012 __isl_keep isl_multi_aff *maff);
5013 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
5014 __isl_take isl_printer *p,
5015 __isl_keep isl_pw_multi_aff *pma);
5016 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
5017 __isl_take isl_printer *p,
5018 __isl_keep isl_union_pw_multi_aff *upma);
5019 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
5020 __isl_take isl_printer *p,
5021 __isl_keep isl_multi_pw_aff *mpa);
5025 Points are elements of a set. They can be used to construct
5026 simple sets (boxes) or they can be used to represent the
5027 individual elements of a set.
5028 The zero point (the origin) can be created using
5030 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
5032 The coordinates of a point can be inspected, set and changed
5035 __isl_give isl_val *isl_point_get_coordinate_val(
5036 __isl_keep isl_point *pnt,
5037 enum isl_dim_type type, int pos);
5038 __isl_give isl_point *isl_point_set_coordinate_val(
5039 __isl_take isl_point *pnt,
5040 enum isl_dim_type type, int pos,
5041 __isl_take isl_val *v);
5043 __isl_give isl_point *isl_point_add_ui(
5044 __isl_take isl_point *pnt,
5045 enum isl_dim_type type, int pos, unsigned val);
5046 __isl_give isl_point *isl_point_sub_ui(
5047 __isl_take isl_point *pnt,
5048 enum isl_dim_type type, int pos, unsigned val);
5050 Other properties can be obtained using
5052 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
5054 Points can be copied or freed using
5056 __isl_give isl_point *isl_point_copy(
5057 __isl_keep isl_point *pnt);
5058 void isl_point_free(__isl_take isl_point *pnt);
5060 A singleton set can be created from a point using
5062 __isl_give isl_basic_set *isl_basic_set_from_point(
5063 __isl_take isl_point *pnt);
5064 __isl_give isl_set *isl_set_from_point(
5065 __isl_take isl_point *pnt);
5067 and a box can be created from two opposite extremal points using
5069 __isl_give isl_basic_set *isl_basic_set_box_from_points(
5070 __isl_take isl_point *pnt1,
5071 __isl_take isl_point *pnt2);
5072 __isl_give isl_set *isl_set_box_from_points(
5073 __isl_take isl_point *pnt1,
5074 __isl_take isl_point *pnt2);
5076 All elements of a B<bounded> (union) set can be enumerated using
5077 the following functions.
5079 int isl_set_foreach_point(__isl_keep isl_set *set,
5080 int (*fn)(__isl_take isl_point *pnt, void *user),
5082 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
5083 int (*fn)(__isl_take isl_point *pnt, void *user),
5086 The function C<fn> is called for each integer point in
5087 C<set> with as second argument the last argument of
5088 the C<isl_set_foreach_point> call. The function C<fn>
5089 should return C<0> on success and C<-1> on failure.
5090 In the latter case, C<isl_set_foreach_point> will stop
5091 enumerating and return C<-1> as well.
5092 If the enumeration is performed successfully and to completion,
5093 then C<isl_set_foreach_point> returns C<0>.
5095 To obtain a single point of a (basic) set, use
5097 __isl_give isl_point *isl_basic_set_sample_point(
5098 __isl_take isl_basic_set *bset);
5099 __isl_give isl_point *isl_set_sample_point(
5100 __isl_take isl_set *set);
5102 If C<set> does not contain any (integer) points, then the
5103 resulting point will be ``void'', a property that can be
5106 int isl_point_is_void(__isl_keep isl_point *pnt);
5108 =head2 Piecewise Quasipolynomials
5110 A piecewise quasipolynomial is a particular kind of function that maps
5111 a parametric point to a rational value.
5112 More specifically, a quasipolynomial is a polynomial expression in greatest
5113 integer parts of affine expressions of parameters and variables.
5114 A piecewise quasipolynomial is a subdivision of a given parametric
5115 domain into disjoint cells with a quasipolynomial associated to
5116 each cell. The value of the piecewise quasipolynomial at a given
5117 point is the value of the quasipolynomial associated to the cell
5118 that contains the point. Outside of the union of cells,
5119 the value is assumed to be zero.
5120 For example, the piecewise quasipolynomial
5122 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
5124 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
5125 A given piecewise quasipolynomial has a fixed domain dimension.
5126 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
5127 defined over different domains.
5128 Piecewise quasipolynomials are mainly used by the C<barvinok>
5129 library for representing the number of elements in a parametric set or map.
5130 For example, the piecewise quasipolynomial above represents
5131 the number of points in the map
5133 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
5135 =head3 Input and Output
5137 Piecewise quasipolynomials can be read from input using
5139 __isl_give isl_union_pw_qpolynomial *
5140 isl_union_pw_qpolynomial_read_from_str(
5141 isl_ctx *ctx, const char *str);
5143 Quasipolynomials and piecewise quasipolynomials can be printed
5144 using the following functions.
5146 __isl_give isl_printer *isl_printer_print_qpolynomial(
5147 __isl_take isl_printer *p,
5148 __isl_keep isl_qpolynomial *qp);
5150 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
5151 __isl_take isl_printer *p,
5152 __isl_keep isl_pw_qpolynomial *pwqp);
5154 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
5155 __isl_take isl_printer *p,
5156 __isl_keep isl_union_pw_qpolynomial *upwqp);
5158 The output format of the printer
5159 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5160 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
5162 In case of printing in C<ISL_FORMAT_C>, the user may want
5163 to set the names of all dimensions
5165 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
5166 __isl_take isl_qpolynomial *qp,
5167 enum isl_dim_type type, unsigned pos,
5169 __isl_give isl_pw_qpolynomial *
5170 isl_pw_qpolynomial_set_dim_name(
5171 __isl_take isl_pw_qpolynomial *pwqp,
5172 enum isl_dim_type type, unsigned pos,
5175 =head3 Creating New (Piecewise) Quasipolynomials
5177 Some simple quasipolynomials can be created using the following functions.
5178 More complicated quasipolynomials can be created by applying
5179 operations such as addition and multiplication
5180 on the resulting quasipolynomials
5182 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
5183 __isl_take isl_space *domain);
5184 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5185 __isl_take isl_space *domain);
5186 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5187 __isl_take isl_space *domain);
5188 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5189 __isl_take isl_space *domain);
5190 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5191 __isl_take isl_space *domain);
5192 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5193 __isl_take isl_space *domain,
5194 __isl_take isl_val *val);
5195 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5196 __isl_take isl_space *domain,
5197 enum isl_dim_type type, unsigned pos);
5198 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5199 __isl_take isl_aff *aff);
5201 Note that the space in which a quasipolynomial lives is a map space
5202 with a one-dimensional range. The C<domain> argument in some of
5203 the functions above corresponds to the domain of this map space.
5205 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5206 with a single cell can be created using the following functions.
5207 Multiple of these single cell piecewise quasipolynomials can
5208 be combined to create more complicated piecewise quasipolynomials.
5210 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5211 __isl_take isl_space *space);
5212 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5213 __isl_take isl_set *set,
5214 __isl_take isl_qpolynomial *qp);
5215 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5216 __isl_take isl_qpolynomial *qp);
5217 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5218 __isl_take isl_pw_aff *pwaff);
5220 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5221 __isl_take isl_space *space);
5222 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5223 __isl_take isl_pw_qpolynomial *pwqp);
5224 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5225 __isl_take isl_union_pw_qpolynomial *upwqp,
5226 __isl_take isl_pw_qpolynomial *pwqp);
5228 Quasipolynomials can be copied and freed again using the following
5231 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5232 __isl_keep isl_qpolynomial *qp);
5233 __isl_null isl_qpolynomial *isl_qpolynomial_free(
5234 __isl_take isl_qpolynomial *qp);
5236 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5237 __isl_keep isl_pw_qpolynomial *pwqp);
5238 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
5239 __isl_take isl_pw_qpolynomial *pwqp);
5241 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5242 __isl_keep isl_union_pw_qpolynomial *upwqp);
5243 __isl_null isl_union_pw_qpolynomial *
5244 isl_union_pw_qpolynomial_free(
5245 __isl_take isl_union_pw_qpolynomial *upwqp);
5247 =head3 Inspecting (Piecewise) Quasipolynomials
5249 To iterate over all piecewise quasipolynomials in a union
5250 piecewise quasipolynomial, use the following function
5252 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5253 __isl_keep isl_union_pw_qpolynomial *upwqp,
5254 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5257 To extract the piecewise quasipolynomial in a given space from a union, use
5259 __isl_give isl_pw_qpolynomial *
5260 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5261 __isl_keep isl_union_pw_qpolynomial *upwqp,
5262 __isl_take isl_space *space);
5264 To iterate over the cells in a piecewise quasipolynomial,
5265 use either of the following two functions
5267 int isl_pw_qpolynomial_foreach_piece(
5268 __isl_keep isl_pw_qpolynomial *pwqp,
5269 int (*fn)(__isl_take isl_set *set,
5270 __isl_take isl_qpolynomial *qp,
5271 void *user), void *user);
5272 int isl_pw_qpolynomial_foreach_lifted_piece(
5273 __isl_keep isl_pw_qpolynomial *pwqp,
5274 int (*fn)(__isl_take isl_set *set,
5275 __isl_take isl_qpolynomial *qp,
5276 void *user), void *user);
5278 As usual, the function C<fn> should return C<0> on success
5279 and C<-1> on failure. The difference between
5280 C<isl_pw_qpolynomial_foreach_piece> and
5281 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5282 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5283 compute unique representations for all existentially quantified
5284 variables and then turn these existentially quantified variables
5285 into extra set variables, adapting the associated quasipolynomial
5286 accordingly. This means that the C<set> passed to C<fn>
5287 will not have any existentially quantified variables, but that
5288 the dimensions of the sets may be different for different
5289 invocations of C<fn>.
5291 The constant term of a quasipolynomial can be extracted using
5293 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5294 __isl_keep isl_qpolynomial *qp);
5296 To iterate over all terms in a quasipolynomial,
5299 int isl_qpolynomial_foreach_term(
5300 __isl_keep isl_qpolynomial *qp,
5301 int (*fn)(__isl_take isl_term *term,
5302 void *user), void *user);
5304 The terms themselves can be inspected and freed using
5307 unsigned isl_term_dim(__isl_keep isl_term *term,
5308 enum isl_dim_type type);
5309 __isl_give isl_val *isl_term_get_coefficient_val(
5310 __isl_keep isl_term *term);
5311 int isl_term_get_exp(__isl_keep isl_term *term,
5312 enum isl_dim_type type, unsigned pos);
5313 __isl_give isl_aff *isl_term_get_div(
5314 __isl_keep isl_term *term, unsigned pos);
5315 void isl_term_free(__isl_take isl_term *term);
5317 Each term is a product of parameters, set variables and
5318 integer divisions. The function C<isl_term_get_exp>
5319 returns the exponent of a given dimensions in the given term.
5321 =head3 Properties of (Piecewise) Quasipolynomials
5323 To check whether two union piecewise quasipolynomials are
5324 obviously equal, use
5326 int isl_union_pw_qpolynomial_plain_is_equal(
5327 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5328 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5330 =head3 Operations on (Piecewise) Quasipolynomials
5332 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5333 __isl_take isl_qpolynomial *qp,
5334 __isl_take isl_val *v);
5335 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5336 __isl_take isl_qpolynomial *qp);
5337 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5338 __isl_take isl_qpolynomial *qp1,
5339 __isl_take isl_qpolynomial *qp2);
5340 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5341 __isl_take isl_qpolynomial *qp1,
5342 __isl_take isl_qpolynomial *qp2);
5343 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5344 __isl_take isl_qpolynomial *qp1,
5345 __isl_take isl_qpolynomial *qp2);
5346 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5347 __isl_take isl_qpolynomial *qp, unsigned exponent);
5349 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5350 __isl_take isl_pw_qpolynomial *pwqp,
5351 enum isl_dim_type type, unsigned n,
5352 __isl_take isl_val *v);
5353 __isl_give isl_pw_qpolynomial *
5354 isl_pw_qpolynomial_scale_val(
5355 __isl_take isl_pw_qpolynomial *pwqp,
5356 __isl_take isl_val *v);
5357 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5358 __isl_take isl_pw_qpolynomial *pwqp1,
5359 __isl_take isl_pw_qpolynomial *pwqp2);
5360 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5361 __isl_take isl_pw_qpolynomial *pwqp1,
5362 __isl_take isl_pw_qpolynomial *pwqp2);
5363 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5364 __isl_take isl_pw_qpolynomial *pwqp1,
5365 __isl_take isl_pw_qpolynomial *pwqp2);
5366 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5367 __isl_take isl_pw_qpolynomial *pwqp);
5368 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5369 __isl_take isl_pw_qpolynomial *pwqp1,
5370 __isl_take isl_pw_qpolynomial *pwqp2);
5371 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5372 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5374 __isl_give isl_union_pw_qpolynomial *
5375 isl_union_pw_qpolynomial_scale_val(
5376 __isl_take isl_union_pw_qpolynomial *upwqp,
5377 __isl_take isl_val *v);
5378 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5379 __isl_take isl_union_pw_qpolynomial *upwqp1,
5380 __isl_take isl_union_pw_qpolynomial *upwqp2);
5381 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5382 __isl_take isl_union_pw_qpolynomial *upwqp1,
5383 __isl_take isl_union_pw_qpolynomial *upwqp2);
5384 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5385 __isl_take isl_union_pw_qpolynomial *upwqp1,
5386 __isl_take isl_union_pw_qpolynomial *upwqp2);
5388 __isl_give isl_val *isl_pw_qpolynomial_eval(
5389 __isl_take isl_pw_qpolynomial *pwqp,
5390 __isl_take isl_point *pnt);
5392 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5393 __isl_take isl_union_pw_qpolynomial *upwqp,
5394 __isl_take isl_point *pnt);
5396 __isl_give isl_set *isl_pw_qpolynomial_domain(
5397 __isl_take isl_pw_qpolynomial *pwqp);
5398 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5399 __isl_take isl_pw_qpolynomial *pwpq,
5400 __isl_take isl_set *set);
5401 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5402 __isl_take isl_pw_qpolynomial *pwpq,
5403 __isl_take isl_set *set);
5405 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5406 __isl_take isl_union_pw_qpolynomial *upwqp);
5407 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5408 __isl_take isl_union_pw_qpolynomial *upwpq,
5409 __isl_take isl_union_set *uset);
5410 __isl_give isl_union_pw_qpolynomial *
5411 isl_union_pw_qpolynomial_intersect_params(
5412 __isl_take isl_union_pw_qpolynomial *upwpq,
5413 __isl_take isl_set *set);
5415 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5416 __isl_take isl_qpolynomial *qp,
5417 __isl_take isl_space *model);
5419 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5420 __isl_take isl_qpolynomial *qp);
5421 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5422 __isl_take isl_pw_qpolynomial *pwqp);
5424 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5425 __isl_take isl_union_pw_qpolynomial *upwqp);
5427 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5428 __isl_take isl_qpolynomial *qp,
5429 __isl_take isl_set *context);
5430 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5431 __isl_take isl_qpolynomial *qp,
5432 __isl_take isl_set *context);
5434 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5435 __isl_take isl_pw_qpolynomial *pwqp,
5436 __isl_take isl_set *context);
5437 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5438 __isl_take isl_pw_qpolynomial *pwqp,
5439 __isl_take isl_set *context);
5441 __isl_give isl_union_pw_qpolynomial *
5442 isl_union_pw_qpolynomial_gist_params(
5443 __isl_take isl_union_pw_qpolynomial *upwqp,
5444 __isl_take isl_set *context);
5445 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5446 __isl_take isl_union_pw_qpolynomial *upwqp,
5447 __isl_take isl_union_set *context);
5449 The gist operation applies the gist operation to each of
5450 the cells in the domain of the input piecewise quasipolynomial.
5451 The context is also exploited
5452 to simplify the quasipolynomials associated to each cell.
5454 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5455 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5456 __isl_give isl_union_pw_qpolynomial *
5457 isl_union_pw_qpolynomial_to_polynomial(
5458 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5460 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5461 the polynomial will be an overapproximation. If C<sign> is negative,
5462 it will be an underapproximation. If C<sign> is zero, the approximation
5463 will lie somewhere in between.
5465 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5467 A piecewise quasipolynomial reduction is a piecewise
5468 reduction (or fold) of quasipolynomials.
5469 In particular, the reduction can be maximum or a minimum.
5470 The objects are mainly used to represent the result of
5471 an upper or lower bound on a quasipolynomial over its domain,
5472 i.e., as the result of the following function.
5474 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5475 __isl_take isl_pw_qpolynomial *pwqp,
5476 enum isl_fold type, int *tight);
5478 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5479 __isl_take isl_union_pw_qpolynomial *upwqp,
5480 enum isl_fold type, int *tight);
5482 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5483 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5484 is the returned bound is known be tight, i.e., for each value
5485 of the parameters there is at least
5486 one element in the domain that reaches the bound.
5487 If the domain of C<pwqp> is not wrapping, then the bound is computed
5488 over all elements in that domain and the result has a purely parametric
5489 domain. If the domain of C<pwqp> is wrapping, then the bound is
5490 computed over the range of the wrapped relation. The domain of the
5491 wrapped relation becomes the domain of the result.
5493 A (piecewise) quasipolynomial reduction can be copied or freed using the
5494 following functions.
5496 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5497 __isl_keep isl_qpolynomial_fold *fold);
5498 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5499 __isl_keep isl_pw_qpolynomial_fold *pwf);
5500 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5501 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5502 void isl_qpolynomial_fold_free(
5503 __isl_take isl_qpolynomial_fold *fold);
5504 __isl_null isl_pw_qpolynomial_fold *
5505 isl_pw_qpolynomial_fold_free(
5506 __isl_take isl_pw_qpolynomial_fold *pwf);
5507 __isl_null isl_union_pw_qpolynomial_fold *
5508 isl_union_pw_qpolynomial_fold_free(
5509 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5511 =head3 Printing Piecewise Quasipolynomial Reductions
5513 Piecewise quasipolynomial reductions can be printed
5514 using the following function.
5516 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5517 __isl_take isl_printer *p,
5518 __isl_keep isl_pw_qpolynomial_fold *pwf);
5519 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5520 __isl_take isl_printer *p,
5521 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5523 For C<isl_printer_print_pw_qpolynomial_fold>,
5524 output format of the printer
5525 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5526 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5527 output format of the printer
5528 needs to be set to C<ISL_FORMAT_ISL>.
5529 In case of printing in C<ISL_FORMAT_C>, the user may want
5530 to set the names of all dimensions
5532 __isl_give isl_pw_qpolynomial_fold *
5533 isl_pw_qpolynomial_fold_set_dim_name(
5534 __isl_take isl_pw_qpolynomial_fold *pwf,
5535 enum isl_dim_type type, unsigned pos,
5538 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5540 To iterate over all piecewise quasipolynomial reductions in a union
5541 piecewise quasipolynomial reduction, use the following function
5543 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5544 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5545 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5546 void *user), void *user);
5548 To iterate over the cells in a piecewise quasipolynomial reduction,
5549 use either of the following two functions
5551 int isl_pw_qpolynomial_fold_foreach_piece(
5552 __isl_keep isl_pw_qpolynomial_fold *pwf,
5553 int (*fn)(__isl_take isl_set *set,
5554 __isl_take isl_qpolynomial_fold *fold,
5555 void *user), void *user);
5556 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5557 __isl_keep isl_pw_qpolynomial_fold *pwf,
5558 int (*fn)(__isl_take isl_set *set,
5559 __isl_take isl_qpolynomial_fold *fold,
5560 void *user), void *user);
5562 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5563 of the difference between these two functions.
5565 To iterate over all quasipolynomials in a reduction, use
5567 int isl_qpolynomial_fold_foreach_qpolynomial(
5568 __isl_keep isl_qpolynomial_fold *fold,
5569 int (*fn)(__isl_take isl_qpolynomial *qp,
5570 void *user), void *user);
5572 =head3 Properties of Piecewise Quasipolynomial Reductions
5574 To check whether two union piecewise quasipolynomial reductions are
5575 obviously equal, use
5577 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5578 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5579 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5581 =head3 Operations on Piecewise Quasipolynomial Reductions
5583 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5584 __isl_take isl_qpolynomial_fold *fold,
5585 __isl_take isl_val *v);
5586 __isl_give isl_pw_qpolynomial_fold *
5587 isl_pw_qpolynomial_fold_scale_val(
5588 __isl_take isl_pw_qpolynomial_fold *pwf,
5589 __isl_take isl_val *v);
5590 __isl_give isl_union_pw_qpolynomial_fold *
5591 isl_union_pw_qpolynomial_fold_scale_val(
5592 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5593 __isl_take isl_val *v);
5595 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5596 __isl_take isl_pw_qpolynomial_fold *pwf1,
5597 __isl_take isl_pw_qpolynomial_fold *pwf2);
5599 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5600 __isl_take isl_pw_qpolynomial_fold *pwf1,
5601 __isl_take isl_pw_qpolynomial_fold *pwf2);
5603 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5604 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5605 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5607 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5608 __isl_take isl_pw_qpolynomial_fold *pwf,
5609 __isl_take isl_point *pnt);
5611 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5612 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5613 __isl_take isl_point *pnt);
5615 __isl_give isl_pw_qpolynomial_fold *
5616 isl_pw_qpolynomial_fold_intersect_params(
5617 __isl_take isl_pw_qpolynomial_fold *pwf,
5618 __isl_take isl_set *set);
5620 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5621 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5622 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5623 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5624 __isl_take isl_union_set *uset);
5625 __isl_give isl_union_pw_qpolynomial_fold *
5626 isl_union_pw_qpolynomial_fold_intersect_params(
5627 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5628 __isl_take isl_set *set);
5630 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5631 __isl_take isl_pw_qpolynomial_fold *pwf);
5633 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5634 __isl_take isl_pw_qpolynomial_fold *pwf);
5636 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5637 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5639 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5640 __isl_take isl_qpolynomial_fold *fold,
5641 __isl_take isl_set *context);
5642 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5643 __isl_take isl_qpolynomial_fold *fold,
5644 __isl_take isl_set *context);
5646 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5647 __isl_take isl_pw_qpolynomial_fold *pwf,
5648 __isl_take isl_set *context);
5649 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5650 __isl_take isl_pw_qpolynomial_fold *pwf,
5651 __isl_take isl_set *context);
5653 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5654 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5655 __isl_take isl_union_set *context);
5656 __isl_give isl_union_pw_qpolynomial_fold *
5657 isl_union_pw_qpolynomial_fold_gist_params(
5658 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5659 __isl_take isl_set *context);
5661 The gist operation applies the gist operation to each of
5662 the cells in the domain of the input piecewise quasipolynomial reduction.
5663 In future, the operation will also exploit the context
5664 to simplify the quasipolynomial reductions associated to each cell.
5666 __isl_give isl_pw_qpolynomial_fold *
5667 isl_set_apply_pw_qpolynomial_fold(
5668 __isl_take isl_set *set,
5669 __isl_take isl_pw_qpolynomial_fold *pwf,
5671 __isl_give isl_pw_qpolynomial_fold *
5672 isl_map_apply_pw_qpolynomial_fold(
5673 __isl_take isl_map *map,
5674 __isl_take isl_pw_qpolynomial_fold *pwf,
5676 __isl_give isl_union_pw_qpolynomial_fold *
5677 isl_union_set_apply_union_pw_qpolynomial_fold(
5678 __isl_take isl_union_set *uset,
5679 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5681 __isl_give isl_union_pw_qpolynomial_fold *
5682 isl_union_map_apply_union_pw_qpolynomial_fold(
5683 __isl_take isl_union_map *umap,
5684 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5687 The functions taking a map
5688 compose the given map with the given piecewise quasipolynomial reduction.
5689 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5690 over all elements in the intersection of the range of the map
5691 and the domain of the piecewise quasipolynomial reduction
5692 as a function of an element in the domain of the map.
5693 The functions taking a set compute a bound over all elements in the
5694 intersection of the set and the domain of the
5695 piecewise quasipolynomial reduction.
5697 =head2 Parametric Vertex Enumeration
5699 The parametric vertex enumeration described in this section
5700 is mainly intended to be used internally and by the C<barvinok>
5703 #include <isl/vertices.h>
5704 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5705 __isl_keep isl_basic_set *bset);
5707 The function C<isl_basic_set_compute_vertices> performs the
5708 actual computation of the parametric vertices and the chamber
5709 decomposition and store the result in an C<isl_vertices> object.
5710 This information can be queried by either iterating over all
5711 the vertices or iterating over all the chambers or cells
5712 and then iterating over all vertices that are active on the chamber.
5714 int isl_vertices_foreach_vertex(
5715 __isl_keep isl_vertices *vertices,
5716 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5719 int isl_vertices_foreach_cell(
5720 __isl_keep isl_vertices *vertices,
5721 int (*fn)(__isl_take isl_cell *cell, void *user),
5723 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5724 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5727 Other operations that can be performed on an C<isl_vertices> object are
5730 isl_ctx *isl_vertices_get_ctx(
5731 __isl_keep isl_vertices *vertices);
5732 int isl_vertices_get_n_vertices(
5733 __isl_keep isl_vertices *vertices);
5734 void isl_vertices_free(__isl_take isl_vertices *vertices);
5736 Vertices can be inspected and destroyed using the following functions.
5738 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5739 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5740 __isl_give isl_basic_set *isl_vertex_get_domain(
5741 __isl_keep isl_vertex *vertex);
5742 __isl_give isl_multi_aff *isl_vertex_get_expr(
5743 __isl_keep isl_vertex *vertex);
5744 void isl_vertex_free(__isl_take isl_vertex *vertex);
5746 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
5747 describing the vertex in terms of the parameters,
5748 while C<isl_vertex_get_domain> returns the activity domain
5751 Chambers can be inspected and destroyed using the following functions.
5753 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5754 __isl_give isl_basic_set *isl_cell_get_domain(
5755 __isl_keep isl_cell *cell);
5756 void isl_cell_free(__isl_take isl_cell *cell);
5758 =head1 Polyhedral Compilation Library
5760 This section collects functionality in C<isl> that has been specifically
5761 designed for use during polyhedral compilation.
5763 =head2 Dependence Analysis
5765 C<isl> contains specialized functionality for performing
5766 array dataflow analysis. That is, given a I<sink> access relation
5767 and a collection of possible I<source> access relations,
5768 C<isl> can compute relations that describe
5769 for each iteration of the sink access, which iteration
5770 of which of the source access relations was the last
5771 to access the same data element before the given iteration
5773 The resulting dependence relations map source iterations
5774 to the corresponding sink iterations.
5775 To compute standard flow dependences, the sink should be
5776 a read, while the sources should be writes.
5777 If any of the source accesses are marked as being I<may>
5778 accesses, then there will be a dependence from the last
5779 I<must> access B<and> from any I<may> access that follows
5780 this last I<must> access.
5781 In particular, if I<all> sources are I<may> accesses,
5782 then memory based dependence analysis is performed.
5783 If, on the other hand, all sources are I<must> accesses,
5784 then value based dependence analysis is performed.
5786 #include <isl/flow.h>
5788 typedef int (*isl_access_level_before)(void *first, void *second);
5790 __isl_give isl_access_info *isl_access_info_alloc(
5791 __isl_take isl_map *sink,
5792 void *sink_user, isl_access_level_before fn,
5794 __isl_give isl_access_info *isl_access_info_add_source(
5795 __isl_take isl_access_info *acc,
5796 __isl_take isl_map *source, int must,
5798 __isl_null isl_access_info *isl_access_info_free(
5799 __isl_take isl_access_info *acc);
5801 __isl_give isl_flow *isl_access_info_compute_flow(
5802 __isl_take isl_access_info *acc);
5804 int isl_flow_foreach(__isl_keep isl_flow *deps,
5805 int (*fn)(__isl_take isl_map *dep, int must,
5806 void *dep_user, void *user),
5808 __isl_give isl_map *isl_flow_get_no_source(
5809 __isl_keep isl_flow *deps, int must);
5810 void isl_flow_free(__isl_take isl_flow *deps);
5812 The function C<isl_access_info_compute_flow> performs the actual
5813 dependence analysis. The other functions are used to construct
5814 the input for this function or to read off the output.
5816 The input is collected in an C<isl_access_info>, which can
5817 be created through a call to C<isl_access_info_alloc>.
5818 The arguments to this functions are the sink access relation
5819 C<sink>, a token C<sink_user> used to identify the sink
5820 access to the user, a callback function for specifying the
5821 relative order of source and sink accesses, and the number
5822 of source access relations that will be added.
5823 The callback function has type C<int (*)(void *first, void *second)>.
5824 The function is called with two user supplied tokens identifying
5825 either a source or the sink and it should return the shared nesting
5826 level and the relative order of the two accesses.
5827 In particular, let I<n> be the number of loops shared by
5828 the two accesses. If C<first> precedes C<second> textually,
5829 then the function should return I<2 * n + 1>; otherwise,
5830 it should return I<2 * n>.
5831 The sources can be added to the C<isl_access_info> by performing
5832 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5833 C<must> indicates whether the source is a I<must> access
5834 or a I<may> access. Note that a multi-valued access relation
5835 should only be marked I<must> if every iteration in the domain
5836 of the relation accesses I<all> elements in its image.
5837 The C<source_user> token is again used to identify
5838 the source access. The range of the source access relation
5839 C<source> should have the same dimension as the range
5840 of the sink access relation.
5841 The C<isl_access_info_free> function should usually not be
5842 called explicitly, because it is called implicitly by
5843 C<isl_access_info_compute_flow>.
5845 The result of the dependence analysis is collected in an
5846 C<isl_flow>. There may be elements of
5847 the sink access for which no preceding source access could be
5848 found or for which all preceding sources are I<may> accesses.
5849 The relations containing these elements can be obtained through
5850 calls to C<isl_flow_get_no_source>, the first with C<must> set
5851 and the second with C<must> unset.
5852 In the case of standard flow dependence analysis,
5853 with the sink a read and the sources I<must> writes,
5854 the first relation corresponds to the reads from uninitialized
5855 array elements and the second relation is empty.
5856 The actual flow dependences can be extracted using
5857 C<isl_flow_foreach>. This function will call the user-specified
5858 callback function C<fn> for each B<non-empty> dependence between
5859 a source and the sink. The callback function is called
5860 with four arguments, the actual flow dependence relation
5861 mapping source iterations to sink iterations, a boolean that
5862 indicates whether it is a I<must> or I<may> dependence, a token
5863 identifying the source and an additional C<void *> with value
5864 equal to the third argument of the C<isl_flow_foreach> call.
5865 A dependence is marked I<must> if it originates from a I<must>
5866 source and if it is not followed by any I<may> sources.
5868 After finishing with an C<isl_flow>, the user should call
5869 C<isl_flow_free> to free all associated memory.
5871 A higher-level interface to dependence analysis is provided
5872 by the following function.
5874 #include <isl/flow.h>
5876 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5877 __isl_take isl_union_map *must_source,
5878 __isl_take isl_union_map *may_source,
5879 __isl_take isl_union_map *schedule,
5880 __isl_give isl_union_map **must_dep,
5881 __isl_give isl_union_map **may_dep,
5882 __isl_give isl_union_map **must_no_source,
5883 __isl_give isl_union_map **may_no_source);
5885 The arrays are identified by the tuple names of the ranges
5886 of the accesses. The iteration domains by the tuple names
5887 of the domains of the accesses and of the schedule.
5888 The relative order of the iteration domains is given by the
5889 schedule. The relations returned through C<must_no_source>
5890 and C<may_no_source> are subsets of C<sink>.
5891 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5892 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5893 any of the other arguments is treated as an error.
5895 =head3 Interaction with Dependence Analysis
5897 During the dependence analysis, we frequently need to perform
5898 the following operation. Given a relation between sink iterations
5899 and potential source iterations from a particular source domain,
5900 what is the last potential source iteration corresponding to each
5901 sink iteration. It can sometimes be convenient to adjust
5902 the set of potential source iterations before or after each such operation.
5903 The prototypical example is fuzzy array dataflow analysis,
5904 where we need to analyze if, based on data-dependent constraints,
5905 the sink iteration can ever be executed without one or more of
5906 the corresponding potential source iterations being executed.
5907 If so, we can introduce extra parameters and select an unknown
5908 but fixed source iteration from the potential source iterations.
5909 To be able to perform such manipulations, C<isl> provides the following
5912 #include <isl/flow.h>
5914 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5915 __isl_keep isl_map *source_map,
5916 __isl_keep isl_set *sink, void *source_user,
5918 __isl_give isl_access_info *isl_access_info_set_restrict(
5919 __isl_take isl_access_info *acc,
5920 isl_access_restrict fn, void *user);
5922 The function C<isl_access_info_set_restrict> should be called
5923 before calling C<isl_access_info_compute_flow> and registers a callback function
5924 that will be called any time C<isl> is about to compute the last
5925 potential source. The first argument is the (reverse) proto-dependence,
5926 mapping sink iterations to potential source iterations.
5927 The second argument represents the sink iterations for which
5928 we want to compute the last source iteration.
5929 The third argument is the token corresponding to the source
5930 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5931 The callback is expected to return a restriction on either the input or
5932 the output of the operation computing the last potential source.
5933 If the input needs to be restricted then restrictions are needed
5934 for both the source and the sink iterations. The sink iterations
5935 and the potential source iterations will be intersected with these sets.
5936 If the output needs to be restricted then only a restriction on the source
5937 iterations is required.
5938 If any error occurs, the callback should return C<NULL>.
5939 An C<isl_restriction> object can be created, freed and inspected
5940 using the following functions.
5942 #include <isl/flow.h>
5944 __isl_give isl_restriction *isl_restriction_input(
5945 __isl_take isl_set *source_restr,
5946 __isl_take isl_set *sink_restr);
5947 __isl_give isl_restriction *isl_restriction_output(
5948 __isl_take isl_set *source_restr);
5949 __isl_give isl_restriction *isl_restriction_none(
5950 __isl_take isl_map *source_map);
5951 __isl_give isl_restriction *isl_restriction_empty(
5952 __isl_take isl_map *source_map);
5953 __isl_null isl_restriction *isl_restriction_free(
5954 __isl_take isl_restriction *restr);
5955 isl_ctx *isl_restriction_get_ctx(
5956 __isl_keep isl_restriction *restr);
5958 C<isl_restriction_none> and C<isl_restriction_empty> are special
5959 cases of C<isl_restriction_input>. C<isl_restriction_none>
5960 is essentially equivalent to
5962 isl_restriction_input(isl_set_universe(
5963 isl_space_range(isl_map_get_space(source_map))),
5965 isl_space_domain(isl_map_get_space(source_map))));
5967 whereas C<isl_restriction_empty> is essentially equivalent to
5969 isl_restriction_input(isl_set_empty(
5970 isl_space_range(isl_map_get_space(source_map))),
5972 isl_space_domain(isl_map_get_space(source_map))));
5976 B<The functionality described in this section is fairly new
5977 and may be subject to change.>
5979 #include <isl/schedule.h>
5980 __isl_give isl_schedule *
5981 isl_schedule_constraints_compute_schedule(
5982 __isl_take isl_schedule_constraints *sc);
5983 __isl_null isl_schedule *isl_schedule_free(
5984 __isl_take isl_schedule *sched);
5986 The function C<isl_schedule_constraints_compute_schedule> can be
5987 used to compute a schedule that satisfy the given schedule constraints.
5988 These schedule constraints include the iteration domain for which
5989 a schedule should be computed and dependences between pairs of
5990 iterations. In particular, these dependences include
5991 I<validity> dependences and I<proximity> dependences.
5992 By default, the algorithm used to construct the schedule is similar
5993 to that of C<Pluto>.
5994 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5996 The generated schedule respects all validity dependences.
5997 That is, all dependence distances over these dependences in the
5998 scheduled space are lexicographically positive.
5999 The default algorithm tries to ensure that the dependence distances
6000 over coincidence constraints are zero and to minimize the
6001 dependence distances over proximity dependences.
6002 Moreover, it tries to obtain sequences (bands) of schedule dimensions
6003 for groups of domains where the dependence distances over validity
6004 dependences have only non-negative values.
6005 When using Feautrier's algorithm, the coincidence and proximity constraints
6006 are only taken into account during the extension to a
6007 full-dimensional schedule.
6009 An C<isl_schedule_constraints> object can be constructed
6010 and manipulated using the following functions.
6012 #include <isl/schedule.h>
6013 __isl_give isl_schedule_constraints *
6014 isl_schedule_constraints_copy(
6015 __isl_keep isl_schedule_constraints *sc);
6016 __isl_give isl_schedule_constraints *
6017 isl_schedule_constraints_on_domain(
6018 __isl_take isl_union_set *domain);
6019 isl_ctx *isl_schedule_constraints_get_ctx(
6020 __isl_keep isl_schedule_constraints *sc);
6021 __isl_give isl_schedule_constraints *
6022 isl_schedule_constraints_set_validity(
6023 __isl_take isl_schedule_constraints *sc,
6024 __isl_take isl_union_map *validity);
6025 __isl_give isl_schedule_constraints *
6026 isl_schedule_constraints_set_coincidence(
6027 __isl_take isl_schedule_constraints *sc,
6028 __isl_take isl_union_map *coincidence);
6029 __isl_give isl_schedule_constraints *
6030 isl_schedule_constraints_set_proximity(
6031 __isl_take isl_schedule_constraints *sc,
6032 __isl_take isl_union_map *proximity);
6033 __isl_give isl_schedule_constraints *
6034 isl_schedule_constraints_set_conditional_validity(
6035 __isl_take isl_schedule_constraints *sc,
6036 __isl_take isl_union_map *condition,
6037 __isl_take isl_union_map *validity);
6038 __isl_null isl_schedule_constraints *
6039 isl_schedule_constraints_free(
6040 __isl_take isl_schedule_constraints *sc);
6042 The initial C<isl_schedule_constraints> object created by
6043 C<isl_schedule_constraints_on_domain> does not impose any constraints.
6044 That is, it has an empty set of dependences.
6045 The function C<isl_schedule_constraints_set_validity> replaces the
6046 validity dependences, mapping domain elements I<i> to domain
6047 elements that should be scheduled after I<i>.
6048 The function C<isl_schedule_constraints_set_coincidence> replaces the
6049 coincidence dependences, mapping domain elements I<i> to domain
6050 elements that should be scheduled together with I<I>, if possible.
6051 The function C<isl_schedule_constraints_set_proximity> replaces the
6052 proximity dependences, mapping domain elements I<i> to domain
6053 elements that should be scheduled either before I<I>
6054 or as early as possible after I<i>.
6056 The function C<isl_schedule_constraints_set_conditional_validity>
6057 replaces the conditional validity constraints.
6058 A conditional validity constraint is only imposed when any of the corresponding
6059 conditions is satisfied, i.e., when any of them is non-zero.
6060 That is, the scheduler ensures that within each band if the dependence
6061 distances over the condition constraints are not all zero
6062 then all corresponding conditional validity constraints are respected.
6063 A conditional validity constraint corresponds to a condition
6064 if the two are adjacent, i.e., if the domain of one relation intersect
6065 the range of the other relation.
6066 The typical use case of conditional validity constraints is
6067 to allow order constraints between live ranges to be violated
6068 as long as the live ranges themselves are local to the band.
6069 To allow more fine-grained control over which conditions correspond
6070 to which conditional validity constraints, the domains and ranges
6071 of these relations may include I<tags>. That is, the domains and
6072 ranges of those relation may themselves be wrapped relations
6073 where the iteration domain appears in the domain of those wrapped relations
6074 and the range of the wrapped relations can be arbitrarily chosen
6075 by the user. Conditions and conditional validity constraints are only
6076 considere adjacent to each other if the entire wrapped relation matches.
6077 In particular, a relation with a tag will never be considered adjacent
6078 to a relation without a tag.
6080 The following function computes a schedule directly from
6081 an iteration domain and validity and proximity dependences
6082 and is implemented in terms of the functions described above.
6083 The use of C<isl_union_set_compute_schedule> is discouraged.
6085 #include <isl/schedule.h>
6086 __isl_give isl_schedule *isl_union_set_compute_schedule(
6087 __isl_take isl_union_set *domain,
6088 __isl_take isl_union_map *validity,
6089 __isl_take isl_union_map *proximity);
6091 A mapping from the domains to the scheduled space can be obtained
6092 from an C<isl_schedule> using the following function.
6094 __isl_give isl_union_map *isl_schedule_get_map(
6095 __isl_keep isl_schedule *sched);
6097 A representation of the schedule can be printed using
6099 __isl_give isl_printer *isl_printer_print_schedule(
6100 __isl_take isl_printer *p,
6101 __isl_keep isl_schedule *schedule);
6103 A representation of the schedule as a forest of bands can be obtained
6104 using the following function.
6106 __isl_give isl_band_list *isl_schedule_get_band_forest(
6107 __isl_keep isl_schedule *schedule);
6109 The individual bands can be visited in depth-first post-order
6110 using the following function.
6112 #include <isl/schedule.h>
6113 int isl_schedule_foreach_band(
6114 __isl_keep isl_schedule *sched,
6115 int (*fn)(__isl_keep isl_band *band, void *user),
6118 The list can be manipulated as explained in L<"Lists">.
6119 The bands inside the list can be copied and freed using the following
6122 #include <isl/band.h>
6123 __isl_give isl_band *isl_band_copy(
6124 __isl_keep isl_band *band);
6125 __isl_null isl_band *isl_band_free(
6126 __isl_take isl_band *band);
6128 Each band contains zero or more scheduling dimensions.
6129 These are referred to as the members of the band.
6130 The section of the schedule that corresponds to the band is
6131 referred to as the partial schedule of the band.
6132 For those nodes that participate in a band, the outer scheduling
6133 dimensions form the prefix schedule, while the inner scheduling
6134 dimensions form the suffix schedule.
6135 That is, if we take a cut of the band forest, then the union of
6136 the concatenations of the prefix, partial and suffix schedules of
6137 each band in the cut is equal to the entire schedule (modulo
6138 some possible padding at the end with zero scheduling dimensions).
6139 The properties of a band can be inspected using the following functions.
6141 #include <isl/band.h>
6142 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
6144 int isl_band_has_children(__isl_keep isl_band *band);
6145 __isl_give isl_band_list *isl_band_get_children(
6146 __isl_keep isl_band *band);
6148 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6149 __isl_keep isl_band *band);
6150 __isl_give isl_union_map *isl_band_get_partial_schedule(
6151 __isl_keep isl_band *band);
6152 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6153 __isl_keep isl_band *band);
6155 int isl_band_n_member(__isl_keep isl_band *band);
6156 int isl_band_member_is_coincident(
6157 __isl_keep isl_band *band, int pos);
6159 int isl_band_list_foreach_band(
6160 __isl_keep isl_band_list *list,
6161 int (*fn)(__isl_keep isl_band *band, void *user),
6164 Note that a scheduling dimension is considered to be ``coincident''
6165 if it satisfies the coincidence constraints within its band.
6166 That is, if the dependence distances of the coincidence
6167 constraints are all zero in that direction (for fixed
6168 iterations of outer bands).
6169 Like C<isl_schedule_foreach_band>,
6170 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6171 in depth-first post-order.
6173 A band can be tiled using the following function.
6175 #include <isl/band.h>
6176 int isl_band_tile(__isl_keep isl_band *band,
6177 __isl_take isl_vec *sizes);
6179 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6181 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6182 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6184 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6186 The C<isl_band_tile> function tiles the band using the given tile sizes
6187 inside its schedule.
6188 A new child band is created to represent the point loops and it is
6189 inserted between the modified band and its children.
6190 The C<tile_scale_tile_loops> option specifies whether the tile
6191 loops iterators should be scaled by the tile sizes.
6192 If the C<tile_shift_point_loops> option is set, then the point loops
6193 are shifted to start at zero.
6195 A band can be split into two nested bands using the following function.
6197 int isl_band_split(__isl_keep isl_band *band, int pos);
6199 The resulting outer band contains the first C<pos> dimensions of C<band>
6200 while the inner band contains the remaining dimensions.
6202 A representation of the band can be printed using
6204 #include <isl/band.h>
6205 __isl_give isl_printer *isl_printer_print_band(
6206 __isl_take isl_printer *p,
6207 __isl_keep isl_band *band);
6211 #include <isl/schedule.h>
6212 int isl_options_set_schedule_max_coefficient(
6213 isl_ctx *ctx, int val);
6214 int isl_options_get_schedule_max_coefficient(
6216 int isl_options_set_schedule_max_constant_term(
6217 isl_ctx *ctx, int val);
6218 int isl_options_get_schedule_max_constant_term(
6220 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6221 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6222 int isl_options_set_schedule_maximize_band_depth(
6223 isl_ctx *ctx, int val);
6224 int isl_options_get_schedule_maximize_band_depth(
6226 int isl_options_set_schedule_outer_coincidence(
6227 isl_ctx *ctx, int val);
6228 int isl_options_get_schedule_outer_coincidence(
6230 int isl_options_set_schedule_split_scaled(
6231 isl_ctx *ctx, int val);
6232 int isl_options_get_schedule_split_scaled(
6234 int isl_options_set_schedule_algorithm(
6235 isl_ctx *ctx, int val);
6236 int isl_options_get_schedule_algorithm(
6238 int isl_options_set_schedule_separate_components(
6239 isl_ctx *ctx, int val);
6240 int isl_options_get_schedule_separate_components(
6245 =item * schedule_max_coefficient
6247 This option enforces that the coefficients for variable and parameter
6248 dimensions in the calculated schedule are not larger than the specified value.
6249 This option can significantly increase the speed of the scheduling calculation
6250 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6251 this option does not introduce bounds on the variable or parameter
6254 =item * schedule_max_constant_term
6256 This option enforces that the constant coefficients in the calculated schedule
6257 are not larger than the maximal constant term. This option can significantly
6258 increase the speed of the scheduling calculation and may also prevent fusing of
6259 unrelated dimensions. A value of -1 means that this option does not introduce
6260 bounds on the constant coefficients.
6262 =item * schedule_fuse
6264 This option controls the level of fusion.
6265 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6266 resulting schedule will be distributed as much as possible.
6267 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6268 try to fuse loops in the resulting schedule.
6270 =item * schedule_maximize_band_depth
6272 If this option is set, we do not split bands at the point
6273 where we detect splitting is necessary. Instead, we
6274 backtrack and split bands as early as possible. This
6275 reduces the number of splits and maximizes the width of
6276 the bands. Wider bands give more possibilities for tiling.
6277 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6278 then bands will be split as early as possible, even if there is no need.
6279 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6281 =item * schedule_outer_coincidence
6283 If this option is set, then we try to construct schedules
6284 where the outermost scheduling dimension in each band
6285 satisfies the coincidence constraints.
6287 =item * schedule_split_scaled
6289 If this option is set, then we try to construct schedules in which the
6290 constant term is split off from the linear part if the linear parts of
6291 the scheduling rows for all nodes in the graphs have a common non-trivial
6293 The constant term is then placed in a separate band and the linear
6296 =item * schedule_algorithm
6298 Selects the scheduling algorithm to be used.
6299 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6300 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6302 =item * schedule_separate_components
6304 If at any point the dependence graph contains any (weakly connected) components,
6305 then these components are scheduled separately.
6306 If this option is not set, then some iterations of the domains
6307 in these components may be scheduled together.
6308 If this option is set, then the components are given consecutive
6313 =head2 AST Generation
6315 This section describes the C<isl> functionality for generating
6316 ASTs that visit all the elements
6317 in a domain in an order specified by a schedule.
6318 In particular, given a C<isl_union_map>, an AST is generated
6319 that visits all the elements in the domain of the C<isl_union_map>
6320 according to the lexicographic order of the corresponding image
6321 element(s). If the range of the C<isl_union_map> consists of
6322 elements in more than one space, then each of these spaces is handled
6323 separately in an arbitrary order.
6324 It should be noted that the image elements only specify the I<order>
6325 in which the corresponding domain elements should be visited.
6326 No direct relation between the image elements and the loop iterators
6327 in the generated AST should be assumed.
6329 Each AST is generated within a build. The initial build
6330 simply specifies the constraints on the parameters (if any)
6331 and can be created, inspected, copied and freed using the following functions.
6333 #include <isl/ast_build.h>
6334 __isl_give isl_ast_build *isl_ast_build_from_context(
6335 __isl_take isl_set *set);
6336 isl_ctx *isl_ast_build_get_ctx(
6337 __isl_keep isl_ast_build *build);
6338 __isl_give isl_ast_build *isl_ast_build_copy(
6339 __isl_keep isl_ast_build *build);
6340 __isl_null isl_ast_build *isl_ast_build_free(
6341 __isl_take isl_ast_build *build);
6343 The C<set> argument is usually a parameter set with zero or more parameters.
6344 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6345 and L</"Fine-grained Control over AST Generation">.
6346 Finally, the AST itself can be constructed using the following
6349 #include <isl/ast_build.h>
6350 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6351 __isl_keep isl_ast_build *build,
6352 __isl_take isl_union_map *schedule);
6354 =head3 Inspecting the AST
6356 The basic properties of an AST node can be obtained as follows.
6358 #include <isl/ast.h>
6359 isl_ctx *isl_ast_node_get_ctx(
6360 __isl_keep isl_ast_node *node);
6361 enum isl_ast_node_type isl_ast_node_get_type(
6362 __isl_keep isl_ast_node *node);
6364 The type of an AST node is one of
6365 C<isl_ast_node_for>,
6367 C<isl_ast_node_block> or
6368 C<isl_ast_node_user>.
6369 An C<isl_ast_node_for> represents a for node.
6370 An C<isl_ast_node_if> represents an if node.
6371 An C<isl_ast_node_block> represents a compound node.
6372 An C<isl_ast_node_user> represents an expression statement.
6373 An expression statement typically corresponds to a domain element, i.e.,
6374 one of the elements that is visited by the AST.
6376 Each type of node has its own additional properties.
6378 #include <isl/ast.h>
6379 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6380 __isl_keep isl_ast_node *node);
6381 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6382 __isl_keep isl_ast_node *node);
6383 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6384 __isl_keep isl_ast_node *node);
6385 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6386 __isl_keep isl_ast_node *node);
6387 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6388 __isl_keep isl_ast_node *node);
6389 int isl_ast_node_for_is_degenerate(
6390 __isl_keep isl_ast_node *node);
6392 An C<isl_ast_for> is considered degenerate if it is known to execute
6395 #include <isl/ast.h>
6396 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6397 __isl_keep isl_ast_node *node);
6398 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6399 __isl_keep isl_ast_node *node);
6400 int isl_ast_node_if_has_else(
6401 __isl_keep isl_ast_node *node);
6402 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6403 __isl_keep isl_ast_node *node);
6405 __isl_give isl_ast_node_list *
6406 isl_ast_node_block_get_children(
6407 __isl_keep isl_ast_node *node);
6409 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6410 __isl_keep isl_ast_node *node);
6412 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6413 the following functions.
6415 #include <isl/ast.h>
6416 isl_ctx *isl_ast_expr_get_ctx(
6417 __isl_keep isl_ast_expr *expr);
6418 enum isl_ast_expr_type isl_ast_expr_get_type(
6419 __isl_keep isl_ast_expr *expr);
6421 The type of an AST expression is one of
6423 C<isl_ast_expr_id> or
6424 C<isl_ast_expr_int>.
6425 An C<isl_ast_expr_op> represents the result of an operation.
6426 An C<isl_ast_expr_id> represents an identifier.
6427 An C<isl_ast_expr_int> represents an integer value.
6429 Each type of expression has its own additional properties.
6431 #include <isl/ast.h>
6432 enum isl_ast_op_type isl_ast_expr_get_op_type(
6433 __isl_keep isl_ast_expr *expr);
6434 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6435 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6436 __isl_keep isl_ast_expr *expr, int pos);
6437 int isl_ast_node_foreach_ast_op_type(
6438 __isl_keep isl_ast_node *node,
6439 int (*fn)(enum isl_ast_op_type type, void *user),
6442 C<isl_ast_expr_get_op_type> returns the type of the operation
6443 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6444 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6446 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6447 C<isl_ast_op_type> that appears in C<node>.
6448 The operation type is one of the following.
6452 =item C<isl_ast_op_and>
6454 Logical I<and> of two arguments.
6455 Both arguments can be evaluated.
6457 =item C<isl_ast_op_and_then>
6459 Logical I<and> of two arguments.
6460 The second argument can only be evaluated if the first evaluates to true.
6462 =item C<isl_ast_op_or>
6464 Logical I<or> of two arguments.
6465 Both arguments can be evaluated.
6467 =item C<isl_ast_op_or_else>
6469 Logical I<or> of two arguments.
6470 The second argument can only be evaluated if the first evaluates to false.
6472 =item C<isl_ast_op_max>
6474 Maximum of two or more arguments.
6476 =item C<isl_ast_op_min>
6478 Minimum of two or more arguments.
6480 =item C<isl_ast_op_minus>
6484 =item C<isl_ast_op_add>
6486 Sum of two arguments.
6488 =item C<isl_ast_op_sub>
6490 Difference of two arguments.
6492 =item C<isl_ast_op_mul>
6494 Product of two arguments.
6496 =item C<isl_ast_op_div>
6498 Exact division. That is, the result is known to be an integer.
6500 =item C<isl_ast_op_fdiv_q>
6502 Result of integer division, rounded towards negative
6505 =item C<isl_ast_op_pdiv_q>
6507 Result of integer division, where dividend is known to be non-negative.
6509 =item C<isl_ast_op_pdiv_r>
6511 Remainder of integer division, where dividend is known to be non-negative.
6513 =item C<isl_ast_op_cond>
6515 Conditional operator defined on three arguments.
6516 If the first argument evaluates to true, then the result
6517 is equal to the second argument. Otherwise, the result
6518 is equal to the third argument.
6519 The second and third argument may only be evaluated if
6520 the first argument evaluates to true and false, respectively.
6521 Corresponds to C<a ? b : c> in C.
6523 =item C<isl_ast_op_select>
6525 Conditional operator defined on three arguments.
6526 If the first argument evaluates to true, then the result
6527 is equal to the second argument. Otherwise, the result
6528 is equal to the third argument.
6529 The second and third argument may be evaluated independently
6530 of the value of the first argument.
6531 Corresponds to C<a * b + (1 - a) * c> in C.
6533 =item C<isl_ast_op_eq>
6537 =item C<isl_ast_op_le>
6539 Less than or equal relation.
6541 =item C<isl_ast_op_lt>
6545 =item C<isl_ast_op_ge>
6547 Greater than or equal relation.
6549 =item C<isl_ast_op_gt>
6551 Greater than relation.
6553 =item C<isl_ast_op_call>
6556 The number of arguments of the C<isl_ast_expr> is one more than
6557 the number of arguments in the function call, the first argument
6558 representing the function being called.
6560 =item C<isl_ast_op_access>
6563 The number of arguments of the C<isl_ast_expr> is one more than
6564 the number of index expressions in the array access, the first argument
6565 representing the array being accessed.
6567 =item C<isl_ast_op_member>
6570 This operation has two arguments, a structure and the name of
6571 the member of the structure being accessed.
6575 #include <isl/ast.h>
6576 __isl_give isl_id *isl_ast_expr_get_id(
6577 __isl_keep isl_ast_expr *expr);
6579 Return the identifier represented by the AST expression.
6581 #include <isl/ast.h>
6582 __isl_give isl_val *isl_ast_expr_get_val(
6583 __isl_keep isl_ast_expr *expr);
6585 Return the integer represented by the AST expression.
6587 =head3 Properties of ASTs
6589 #include <isl/ast.h>
6590 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6591 __isl_keep isl_ast_expr *expr2);
6593 Check if two C<isl_ast_expr>s are equal to each other.
6595 =head3 Manipulating and printing the AST
6597 AST nodes can be copied and freed using the following functions.
6599 #include <isl/ast.h>
6600 __isl_give isl_ast_node *isl_ast_node_copy(
6601 __isl_keep isl_ast_node *node);
6602 __isl_null isl_ast_node *isl_ast_node_free(
6603 __isl_take isl_ast_node *node);
6605 AST expressions can be copied and freed using the following functions.
6607 #include <isl/ast.h>
6608 __isl_give isl_ast_expr *isl_ast_expr_copy(
6609 __isl_keep isl_ast_expr *expr);
6610 __isl_null isl_ast_expr *isl_ast_expr_free(
6611 __isl_take isl_ast_expr *expr);
6613 New AST expressions can be created either directly or within
6614 the context of an C<isl_ast_build>.
6616 #include <isl/ast.h>
6617 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6618 __isl_take isl_val *v);
6619 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6620 __isl_take isl_id *id);
6621 __isl_give isl_ast_expr *isl_ast_expr_neg(
6622 __isl_take isl_ast_expr *expr);
6623 __isl_give isl_ast_expr *isl_ast_expr_add(
6624 __isl_take isl_ast_expr *expr1,
6625 __isl_take isl_ast_expr *expr2);
6626 __isl_give isl_ast_expr *isl_ast_expr_sub(
6627 __isl_take isl_ast_expr *expr1,
6628 __isl_take isl_ast_expr *expr2);
6629 __isl_give isl_ast_expr *isl_ast_expr_mul(
6630 __isl_take isl_ast_expr *expr1,
6631 __isl_take isl_ast_expr *expr2);
6632 __isl_give isl_ast_expr *isl_ast_expr_div(
6633 __isl_take isl_ast_expr *expr1,
6634 __isl_take isl_ast_expr *expr2);
6635 __isl_give isl_ast_expr *isl_ast_expr_and(
6636 __isl_take isl_ast_expr *expr1,
6637 __isl_take isl_ast_expr *expr2)
6638 __isl_give isl_ast_expr *isl_ast_expr_or(
6639 __isl_take isl_ast_expr *expr1,
6640 __isl_take isl_ast_expr *expr2)
6641 __isl_give isl_ast_expr *isl_ast_expr_access(
6642 __isl_take isl_ast_expr *array,
6643 __isl_take isl_ast_expr_list *indices);
6645 #include <isl/ast_build.h>
6646 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6647 __isl_keep isl_ast_build *build,
6648 __isl_take isl_pw_aff *pa);
6649 __isl_give isl_ast_expr *
6650 isl_ast_build_access_from_pw_multi_aff(
6651 __isl_keep isl_ast_build *build,
6652 __isl_take isl_pw_multi_aff *pma);
6653 __isl_give isl_ast_expr *
6654 isl_ast_build_access_from_multi_pw_aff(
6655 __isl_keep isl_ast_build *build,
6656 __isl_take isl_multi_pw_aff *mpa);
6657 __isl_give isl_ast_expr *
6658 isl_ast_build_call_from_pw_multi_aff(
6659 __isl_keep isl_ast_build *build,
6660 __isl_take isl_pw_multi_aff *pma);
6661 __isl_give isl_ast_expr *
6662 isl_ast_build_call_from_multi_pw_aff(
6663 __isl_keep isl_ast_build *build,
6664 __isl_take isl_multi_pw_aff *mpa);
6666 The domains of C<pa>, C<mpa> and C<pma> should correspond
6667 to the schedule space of C<build>.
6668 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6669 the function being called.
6670 If the accessed space is a nested relation, then it is taken
6671 to represent an access of the member specified by the range
6672 of this nested relation of the structure specified by the domain
6673 of the nested relation.
6675 The following functions can be used to modify an C<isl_ast_expr>.
6677 #include <isl/ast.h>
6678 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6679 __isl_take isl_ast_expr *expr, int pos,
6680 __isl_take isl_ast_expr *arg);
6682 Replace the argument of C<expr> at position C<pos> by C<arg>.
6684 #include <isl/ast.h>
6685 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6686 __isl_take isl_ast_expr *expr,
6687 __isl_take isl_id_to_ast_expr *id2expr);
6689 The function C<isl_ast_expr_substitute_ids> replaces the
6690 subexpressions of C<expr> of type C<isl_ast_expr_id>
6691 by the corresponding expression in C<id2expr>, if there is any.
6694 User specified data can be attached to an C<isl_ast_node> and obtained
6695 from the same C<isl_ast_node> using the following functions.
6697 #include <isl/ast.h>
6698 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6699 __isl_take isl_ast_node *node,
6700 __isl_take isl_id *annotation);
6701 __isl_give isl_id *isl_ast_node_get_annotation(
6702 __isl_keep isl_ast_node *node);
6704 Basic printing can be performed using the following functions.
6706 #include <isl/ast.h>
6707 __isl_give isl_printer *isl_printer_print_ast_expr(
6708 __isl_take isl_printer *p,
6709 __isl_keep isl_ast_expr *expr);
6710 __isl_give isl_printer *isl_printer_print_ast_node(
6711 __isl_take isl_printer *p,
6712 __isl_keep isl_ast_node *node);
6714 More advanced printing can be performed using the following functions.
6716 #include <isl/ast.h>
6717 __isl_give isl_printer *isl_ast_op_type_print_macro(
6718 enum isl_ast_op_type type,
6719 __isl_take isl_printer *p);
6720 __isl_give isl_printer *isl_ast_node_print_macros(
6721 __isl_keep isl_ast_node *node,
6722 __isl_take isl_printer *p);
6723 __isl_give isl_printer *isl_ast_node_print(
6724 __isl_keep isl_ast_node *node,
6725 __isl_take isl_printer *p,
6726 __isl_take isl_ast_print_options *options);
6727 __isl_give isl_printer *isl_ast_node_for_print(
6728 __isl_keep isl_ast_node *node,
6729 __isl_take isl_printer *p,
6730 __isl_take isl_ast_print_options *options);
6731 __isl_give isl_printer *isl_ast_node_if_print(
6732 __isl_keep isl_ast_node *node,
6733 __isl_take isl_printer *p,
6734 __isl_take isl_ast_print_options *options);
6736 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6737 C<isl> may print out an AST that makes use of macros such
6738 as C<floord>, C<min> and C<max>.
6739 C<isl_ast_op_type_print_macro> prints out the macro
6740 corresponding to a specific C<isl_ast_op_type>.
6741 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6742 for expressions where these macros would be used and prints
6743 out the required macro definitions.
6744 Essentially, C<isl_ast_node_print_macros> calls
6745 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6746 as function argument.
6747 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6748 C<isl_ast_node_if_print> print an C<isl_ast_node>
6749 in C<ISL_FORMAT_C>, but allow for some extra control
6750 through an C<isl_ast_print_options> object.
6751 This object can be created using the following functions.
6753 #include <isl/ast.h>
6754 __isl_give isl_ast_print_options *
6755 isl_ast_print_options_alloc(isl_ctx *ctx);
6756 __isl_give isl_ast_print_options *
6757 isl_ast_print_options_copy(
6758 __isl_keep isl_ast_print_options *options);
6759 __isl_null isl_ast_print_options *
6760 isl_ast_print_options_free(
6761 __isl_take isl_ast_print_options *options);
6763 __isl_give isl_ast_print_options *
6764 isl_ast_print_options_set_print_user(
6765 __isl_take isl_ast_print_options *options,
6766 __isl_give isl_printer *(*print_user)(
6767 __isl_take isl_printer *p,
6768 __isl_take isl_ast_print_options *options,
6769 __isl_keep isl_ast_node *node, void *user),
6771 __isl_give isl_ast_print_options *
6772 isl_ast_print_options_set_print_for(
6773 __isl_take isl_ast_print_options *options,
6774 __isl_give isl_printer *(*print_for)(
6775 __isl_take isl_printer *p,
6776 __isl_take isl_ast_print_options *options,
6777 __isl_keep isl_ast_node *node, void *user),
6780 The callback set by C<isl_ast_print_options_set_print_user>
6781 is called whenever a node of type C<isl_ast_node_user> needs to
6783 The callback set by C<isl_ast_print_options_set_print_for>
6784 is called whenever a node of type C<isl_ast_node_for> needs to
6786 Note that C<isl_ast_node_for_print> will I<not> call the
6787 callback set by C<isl_ast_print_options_set_print_for> on the node
6788 on which C<isl_ast_node_for_print> is called, but only on nested
6789 nodes of type C<isl_ast_node_for>. It is therefore safe to
6790 call C<isl_ast_node_for_print> from within the callback set by
6791 C<isl_ast_print_options_set_print_for>.
6793 The following option determines the type to be used for iterators
6794 while printing the AST.
6796 int isl_options_set_ast_iterator_type(
6797 isl_ctx *ctx, const char *val);
6798 const char *isl_options_get_ast_iterator_type(
6803 #include <isl/ast_build.h>
6804 int isl_options_set_ast_build_atomic_upper_bound(
6805 isl_ctx *ctx, int val);
6806 int isl_options_get_ast_build_atomic_upper_bound(
6808 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6810 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6811 int isl_options_set_ast_build_exploit_nested_bounds(
6812 isl_ctx *ctx, int val);
6813 int isl_options_get_ast_build_exploit_nested_bounds(
6815 int isl_options_set_ast_build_group_coscheduled(
6816 isl_ctx *ctx, int val);
6817 int isl_options_get_ast_build_group_coscheduled(
6819 int isl_options_set_ast_build_scale_strides(
6820 isl_ctx *ctx, int val);
6821 int isl_options_get_ast_build_scale_strides(
6823 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6825 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6826 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6828 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6832 =item * ast_build_atomic_upper_bound
6834 Generate loop upper bounds that consist of the current loop iterator,
6835 an operator and an expression not involving the iterator.
6836 If this option is not set, then the current loop iterator may appear
6837 several times in the upper bound.
6838 For example, when this option is turned off, AST generation
6841 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6845 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6848 When the option is turned on, the following AST is generated
6850 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6853 =item * ast_build_prefer_pdiv
6855 If this option is turned off, then the AST generation will
6856 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6857 operators, but no C<isl_ast_op_pdiv_q> or
6858 C<isl_ast_op_pdiv_r> operators.
6859 If this options is turned on, then C<isl> will try to convert
6860 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6861 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6863 =item * ast_build_exploit_nested_bounds
6865 Simplify conditions based on bounds of nested for loops.
6866 In particular, remove conditions that are implied by the fact
6867 that one or more nested loops have at least one iteration,
6868 meaning that the upper bound is at least as large as the lower bound.
6869 For example, when this option is turned off, AST generation
6872 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6878 for (int c0 = 0; c0 <= N; c0 += 1)
6879 for (int c1 = 0; c1 <= M; c1 += 1)
6882 When the option is turned on, the following AST is generated
6884 for (int c0 = 0; c0 <= N; c0 += 1)
6885 for (int c1 = 0; c1 <= M; c1 += 1)
6888 =item * ast_build_group_coscheduled
6890 If two domain elements are assigned the same schedule point, then
6891 they may be executed in any order and they may even appear in different
6892 loops. If this options is set, then the AST generator will make
6893 sure that coscheduled domain elements do not appear in separate parts
6894 of the AST. This is useful in case of nested AST generation
6895 if the outer AST generation is given only part of a schedule
6896 and the inner AST generation should handle the domains that are
6897 coscheduled by this initial part of the schedule together.
6898 For example if an AST is generated for a schedule
6900 { A[i] -> [0]; B[i] -> [0] }
6902 then the C<isl_ast_build_set_create_leaf> callback described
6903 below may get called twice, once for each domain.
6904 Setting this option ensures that the callback is only called once
6905 on both domains together.
6907 =item * ast_build_separation_bounds
6909 This option specifies which bounds to use during separation.
6910 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6911 then all (possibly implicit) bounds on the current dimension will
6912 be used during separation.
6913 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6914 then only those bounds that are explicitly available will
6915 be used during separation.
6917 =item * ast_build_scale_strides
6919 This option specifies whether the AST generator is allowed
6920 to scale down iterators of strided loops.
6922 =item * ast_build_allow_else
6924 This option specifies whether the AST generator is allowed
6925 to construct if statements with else branches.
6927 =item * ast_build_allow_or
6929 This option specifies whether the AST generator is allowed
6930 to construct if conditions with disjunctions.
6934 =head3 Fine-grained Control over AST Generation
6936 Besides specifying the constraints on the parameters,
6937 an C<isl_ast_build> object can be used to control
6938 various aspects of the AST generation process.
6939 The most prominent way of control is through ``options'',
6940 which can be set using the following function.
6942 #include <isl/ast_build.h>
6943 __isl_give isl_ast_build *
6944 isl_ast_build_set_options(
6945 __isl_take isl_ast_build *control,
6946 __isl_take isl_union_map *options);
6948 The options are encoded in an <isl_union_map>.
6949 The domain of this union relation refers to the schedule domain,
6950 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6951 In the case of nested AST generation (see L</"Nested AST Generation">),
6952 the domain of C<options> should refer to the extra piece of the schedule.
6953 That is, it should be equal to the range of the wrapped relation in the
6954 range of the schedule.
6955 The range of the options can consist of elements in one or more spaces,
6956 the names of which determine the effect of the option.
6957 The values of the range typically also refer to the schedule dimension
6958 to which the option applies. In case of nested AST generation
6959 (see L</"Nested AST Generation">), these values refer to the position
6960 of the schedule dimension within the innermost AST generation.
6961 The constraints on the domain elements of
6962 the option should only refer to this dimension and earlier dimensions.
6963 We consider the following spaces.
6967 =item C<separation_class>
6969 This space is a wrapped relation between two one dimensional spaces.
6970 The input space represents the schedule dimension to which the option
6971 applies and the output space represents the separation class.
6972 While constructing a loop corresponding to the specified schedule
6973 dimension(s), the AST generator will try to generate separate loops
6974 for domain elements that are assigned different classes.
6975 If only some of the elements are assigned a class, then those elements
6976 that are not assigned any class will be treated as belonging to a class
6977 that is separate from the explicitly assigned classes.
6978 The typical use case for this option is to separate full tiles from
6980 The other options, described below, are applied after the separation
6983 As an example, consider the separation into full and partial tiles
6984 of a tiling of a triangular domain.
6985 Take, for example, the domain
6987 { A[i,j] : 0 <= i,j and i + j <= 100 }
6989 and a tiling into tiles of 10 by 10. The input to the AST generator
6990 is then the schedule
6992 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6995 Without any options, the following AST is generated
6997 for (int c0 = 0; c0 <= 10; c0 += 1)
6998 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6999 for (int c2 = 10 * c0;
7000 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7002 for (int c3 = 10 * c1;
7003 c3 <= min(10 * c1 + 9, -c2 + 100);
7007 Separation into full and partial tiles can be obtained by assigning
7008 a class, say C<0>, to the full tiles. The full tiles are represented by those
7009 values of the first and second schedule dimensions for which there are
7010 values of the third and fourth dimensions to cover an entire tile.
7011 That is, we need to specify the following option
7013 { [a,b,c,d] -> separation_class[[0]->[0]] :
7014 exists b': 0 <= 10a,10b' and
7015 10a+9+10b'+9 <= 100;
7016 [a,b,c,d] -> separation_class[[1]->[0]] :
7017 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
7021 { [a, b, c, d] -> separation_class[[1] -> [0]] :
7022 a >= 0 and b >= 0 and b <= 8 - a;
7023 [a, b, c, d] -> separation_class[[0] -> [0]] :
7026 With this option, the generated AST is as follows
7029 for (int c0 = 0; c0 <= 8; c0 += 1) {
7030 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
7031 for (int c2 = 10 * c0;
7032 c2 <= 10 * c0 + 9; c2 += 1)
7033 for (int c3 = 10 * c1;
7034 c3 <= 10 * c1 + 9; c3 += 1)
7036 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
7037 for (int c2 = 10 * c0;
7038 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7040 for (int c3 = 10 * c1;
7041 c3 <= min(-c2 + 100, 10 * c1 + 9);
7045 for (int c0 = 9; c0 <= 10; c0 += 1)
7046 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7047 for (int c2 = 10 * c0;
7048 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7050 for (int c3 = 10 * c1;
7051 c3 <= min(10 * c1 + 9, -c2 + 100);
7058 This is a single-dimensional space representing the schedule dimension(s)
7059 to which ``separation'' should be applied. Separation tries to split
7060 a loop into several pieces if this can avoid the generation of guards
7062 See also the C<atomic> option.
7066 This is a single-dimensional space representing the schedule dimension(s)
7067 for which the domains should be considered ``atomic''. That is, the
7068 AST generator will make sure that any given domain space will only appear
7069 in a single loop at the specified level.
7071 Consider the following schedule
7073 { a[i] -> [i] : 0 <= i < 10;
7074 b[i] -> [i+1] : 0 <= i < 10 }
7076 If the following option is specified
7078 { [i] -> separate[x] }
7080 then the following AST will be generated
7084 for (int c0 = 1; c0 <= 9; c0 += 1) {
7091 If, on the other hand, the following option is specified
7093 { [i] -> atomic[x] }
7095 then the following AST will be generated
7097 for (int c0 = 0; c0 <= 10; c0 += 1) {
7104 If neither C<atomic> nor C<separate> is specified, then the AST generator
7105 may produce either of these two results or some intermediate form.
7109 This is a single-dimensional space representing the schedule dimension(s)
7110 that should be I<completely> unrolled.
7111 To obtain a partial unrolling, the user should apply an additional
7112 strip-mining to the schedule and fully unroll the inner loop.
7116 Additional control is available through the following functions.
7118 #include <isl/ast_build.h>
7119 __isl_give isl_ast_build *
7120 isl_ast_build_set_iterators(
7121 __isl_take isl_ast_build *control,
7122 __isl_take isl_id_list *iterators);
7124 The function C<isl_ast_build_set_iterators> allows the user to
7125 specify a list of iterator C<isl_id>s to be used as iterators.
7126 If the input schedule is injective, then
7127 the number of elements in this list should be as large as the dimension
7128 of the schedule space, but no direct correspondence should be assumed
7129 between dimensions and elements.
7130 If the input schedule is not injective, then an additional number
7131 of C<isl_id>s equal to the largest dimension of the input domains
7133 If the number of provided C<isl_id>s is insufficient, then additional
7134 names are automatically generated.
7136 #include <isl/ast_build.h>
7137 __isl_give isl_ast_build *
7138 isl_ast_build_set_create_leaf(
7139 __isl_take isl_ast_build *control,
7140 __isl_give isl_ast_node *(*fn)(
7141 __isl_take isl_ast_build *build,
7142 void *user), void *user);
7145 C<isl_ast_build_set_create_leaf> function allows for the
7146 specification of a callback that should be called whenever the AST
7147 generator arrives at an element of the schedule domain.
7148 The callback should return an AST node that should be inserted
7149 at the corresponding position of the AST. The default action (when
7150 the callback is not set) is to continue generating parts of the AST to scan
7151 all the domain elements associated to the schedule domain element
7152 and to insert user nodes, ``calling'' the domain element, for each of them.
7153 The C<build> argument contains the current state of the C<isl_ast_build>.
7154 To ease nested AST generation (see L</"Nested AST Generation">),
7155 all control information that is
7156 specific to the current AST generation such as the options and
7157 the callbacks has been removed from this C<isl_ast_build>.
7158 The callback would typically return the result of a nested
7160 user defined node created using the following function.
7162 #include <isl/ast.h>
7163 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7164 __isl_take isl_ast_expr *expr);
7166 #include <isl/ast_build.h>
7167 __isl_give isl_ast_build *
7168 isl_ast_build_set_at_each_domain(
7169 __isl_take isl_ast_build *build,
7170 __isl_give isl_ast_node *(*fn)(
7171 __isl_take isl_ast_node *node,
7172 __isl_keep isl_ast_build *build,
7173 void *user), void *user);
7174 __isl_give isl_ast_build *
7175 isl_ast_build_set_before_each_for(
7176 __isl_take isl_ast_build *build,
7177 __isl_give isl_id *(*fn)(
7178 __isl_keep isl_ast_build *build,
7179 void *user), void *user);
7180 __isl_give isl_ast_build *
7181 isl_ast_build_set_after_each_for(
7182 __isl_take isl_ast_build *build,
7183 __isl_give isl_ast_node *(*fn)(
7184 __isl_take isl_ast_node *node,
7185 __isl_keep isl_ast_build *build,
7186 void *user), void *user);
7188 The callback set by C<isl_ast_build_set_at_each_domain> will
7189 be called for each domain AST node.
7190 The callbacks set by C<isl_ast_build_set_before_each_for>
7191 and C<isl_ast_build_set_after_each_for> will be called
7192 for each for AST node. The first will be called in depth-first
7193 pre-order, while the second will be called in depth-first post-order.
7194 Since C<isl_ast_build_set_before_each_for> is called before the for
7195 node is actually constructed, it is only passed an C<isl_ast_build>.
7196 The returned C<isl_id> will be added as an annotation (using
7197 C<isl_ast_node_set_annotation>) to the constructed for node.
7198 In particular, if the user has also specified an C<after_each_for>
7199 callback, then the annotation can be retrieved from the node passed to
7200 that callback using C<isl_ast_node_get_annotation>.
7201 All callbacks should C<NULL> on failure.
7202 The given C<isl_ast_build> can be used to create new
7203 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7204 or C<isl_ast_build_call_from_pw_multi_aff>.
7206 =head3 Nested AST Generation
7208 C<isl> allows the user to create an AST within the context
7209 of another AST. These nested ASTs are created using the
7210 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7211 outer AST. The C<build> argument should be an C<isl_ast_build>
7212 passed to a callback set by
7213 C<isl_ast_build_set_create_leaf>.
7214 The space of the range of the C<schedule> argument should refer
7215 to this build. In particular, the space should be a wrapped
7216 relation and the domain of this wrapped relation should be the
7217 same as that of the range of the schedule returned by
7218 C<isl_ast_build_get_schedule> below.
7219 In practice, the new schedule is typically
7220 created by calling C<isl_union_map_range_product> on the old schedule
7221 and some extra piece of the schedule.
7222 The space of the schedule domain is also available from
7223 the C<isl_ast_build>.
7225 #include <isl/ast_build.h>
7226 __isl_give isl_union_map *isl_ast_build_get_schedule(
7227 __isl_keep isl_ast_build *build);
7228 __isl_give isl_space *isl_ast_build_get_schedule_space(
7229 __isl_keep isl_ast_build *build);
7230 __isl_give isl_ast_build *isl_ast_build_restrict(
7231 __isl_take isl_ast_build *build,
7232 __isl_take isl_set *set);
7234 The C<isl_ast_build_get_schedule> function returns a (partial)
7235 schedule for the domains elements for which part of the AST still needs to
7236 be generated in the current build.
7237 In particular, the domain elements are mapped to those iterations of the loops
7238 enclosing the current point of the AST generation inside which
7239 the domain elements are executed.
7240 No direct correspondence between
7241 the input schedule and this schedule should be assumed.
7242 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7243 to create a set for C<isl_ast_build_restrict> to intersect
7244 with the current build. In particular, the set passed to
7245 C<isl_ast_build_restrict> can have additional parameters.
7246 The ids of the set dimensions in the space returned by
7247 C<isl_ast_build_get_schedule_space> correspond to the
7248 iterators of the already generated loops.
7249 The user should not rely on the ids of the output dimensions
7250 of the relations in the union relation returned by
7251 C<isl_ast_build_get_schedule> having any particular value.
7255 Although C<isl> is mainly meant to be used as a library,
7256 it also contains some basic applications that use some
7257 of the functionality of C<isl>.
7258 The input may be specified in either the L<isl format>
7259 or the L<PolyLib format>.
7261 =head2 C<isl_polyhedron_sample>
7263 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7264 an integer element of the polyhedron, if there is any.
7265 The first column in the output is the denominator and is always
7266 equal to 1. If the polyhedron contains no integer points,
7267 then a vector of length zero is printed.
7271 C<isl_pip> takes the same input as the C<example> program
7272 from the C<piplib> distribution, i.e., a set of constraints
7273 on the parameters, a line containing only -1 and finally a set
7274 of constraints on a parametric polyhedron.
7275 The coefficients of the parameters appear in the last columns
7276 (but before the final constant column).
7277 The output is the lexicographic minimum of the parametric polyhedron.
7278 As C<isl> currently does not have its own output format, the output
7279 is just a dump of the internal state.
7281 =head2 C<isl_polyhedron_minimize>
7283 C<isl_polyhedron_minimize> computes the minimum of some linear
7284 or affine objective function over the integer points in a polyhedron.
7285 If an affine objective function
7286 is given, then the constant should appear in the last column.
7288 =head2 C<isl_polytope_scan>
7290 Given a polytope, C<isl_polytope_scan> prints
7291 all integer points in the polytope.
7293 =head2 C<isl_codegen>
7295 Given a schedule, a context set and an options relation,
7296 C<isl_codegen> prints out an AST that scans the domain elements
7297 of the schedule in the order of their image(s) taking into account
7298 the constraints in the context set.